Advanced fractional differential and integral equations

Advanced Fractional Differential and Integral Equations

Volumn , Issue , 2014, Pages 1-362

  Abbas, Said ^a,b   Benchohra, Mouffak ^a,c   N'Guerekata, Gaston Mandata ^a,d  

^a MORGAN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF SAIDA   (Algeria)

^c NONE   (Saudi Arabia)

^d NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84952776487     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (380)

1. S. Abbas, D. Baleanu and M. Benchohra, Global attractivity for fractional order delay partial integro-differential equations, Adv. Difference Equ. 2012, 19 pages doi:10.1186/1687-1847-2012-62.
2. S. Abbas and M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst. 3 (2009), 597-604.
3. S. Abbas and M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative, Commun.Math. Anal. 7 (2009), 62-72.
4. S. Abbas and M. Benchohra, Upper and lower solutionsmethod for impulsive partial hyperbolic differential equations with fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010), 406-413.
5. S. Abbas and M. Benchohra, The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses, Discuss. Math. Differ. Incl. Control Optim. 30 (1) (2010), 141-161.
6. S. Abbas and M. Benchohra, Impulsive partial hyperbolic differential inclusions of fractional order, Demonstratio Math. XLIII (4) (2010), 775-797.
7. S. Abbas and M. Benchohra, Darboux problem for partial functional differential equations with infinite delay and Caputo's fractional derivative, Adv. Dyn. Syst. Appl. 5 (1) (2010), 1-19.
8. S. Abbas and M. Benchohra, Impulsive partial hyperbolic functional differential equations of fractional order with state-dependent delay, Frac. Calc. Appl. Anal. 13 (3) (2010), 225-244.
9. S. Abbas and M. Benchohra, Upper and lower solutions method for the darboux problem for fractional order partial differential inclusions, Int. J. ModernMath. 5 (3) (2010), 327-338.
10. S. Abbas and M. Benchohra, Upper and lower solutionsmethod for partial hyperbolic functional differential equations with Caputo's fractional derivative, Libertas Math. 31 (2011), 103-110.
11. S. Abbas and M. Benchohra, Darboux problem for implicit impulsive partial hyperbolic differential equations, Electron. J. Differential Equations 2011 (2011), 15 pp.
12. S. Abbas and M. Benchohra, On the set of solutions of fractional order Riemann-Liouville integral inclusions, Demonst ratio Math. XLVI (2) (2013), 271-281.
13. S. Abbas and M. Benchohra, On the set of solutions for the Darboux problem for fractional order partial hyperbolic functional differential inclusions, Fixed Point Theory 14 (2) (2013), 253-262.
14. S. Abbas and M. Benchohra, Fractional order Riemann-Liouville integral equations with multiple time delay, Appl. Math. E-Notes 12 (2012), 79-87.
15. S. Abbas and M. Benchohra, Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay, Opuscula Math. 33 (2) (2013), 209-222.
16. S. Abbas and M. Benchohra, On the existence and local asymptotic stability of solutions of fractional order integral equations, Comment. Math. 52 (1) (2012), 91-100.
17. S. Abbas and M. Benchohra, Fractional Order partial hyperbolic differential equations involving Caputo's derivative, Stud. Univ. Babeş-Bolyai Math. 54 (2012), 469-479.
18. S. Abbas and M. Benchohra, Impulsive partial functional integro-differential equations of fractional order, Commun. Appl. Anal. 16 (2) (2012), 249-260.
19. S. Abbas and M. Benchohra, Global stability results for nonlinear partial fractional order Riemann-Liouville Volterra-Stieltjes functional integral equations, Math. Sci. Res. J. 16 (2012), 82-92.
20. S. Abbas and M. Benchohra, Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order, Nonlinear Anal. Forum 17 (2012), 107-115.
21. S. Abbas and M. Benchohra, A global uniqueness result for fractional order implicit differential equations, Comment. Math. Univ. Carolinae 53 (2012), 605-614.
22. S. Abbas and M. Benchohra, Uniqueness results for Fredholm type fractional order Riemann-Liouville integral equations, FasciculiMath. 51 (2013), 5-19.
23. S. Abbas and M. Benchohra, Existence and stability for partial functional integrodifferential equations of fractional order with multiple time delay, Nonlinear Studies 20 (2) (2013), 149-162.
24. S. Abbas and M. Benchohra, Global asymptotic stability for nonlinear multi-delay differential equations of fractional order, Proc. A. Ramadze Math. Inst. 161 (2013), 1-13.
25. S. Abbas and M. Benchohra, Fractional order integral equations of two independent variables, Appl. Math. Comput. 227 (2014), 755-761.
26. S. Abbas and M. Benchohra, Qualitative theory for fractional order Riemann-Liouville integral equations in two independent variables, Tamsui Oxford J. Inf. Math. Sci. 29 (2), (2013),.
27. S. Abbas and M. Benchohra, Nonlinear fractional order Riemann-LiouvilleVolterra-Stieltjes partial integral equations on unbounded domains, Commun. Math. Anal. 14 (1) (2013), 104-117.
28. S. Abbas and M. Benchohra, Existence and stability of nonlinear fractional order Riemann-Liouville Volterra-Stieltjes multi-delay lntegral equations, J. Integral Equ. Appl., 25 (2) (2013), 143-158.
29. S. Abbas and M. Benchohra, Ulam-Hyers stability for the Darboux problem for partial fractional differential and Integro-differential equations via Picard operators, Results. Math. 65 (1-2) (2014), 67-79.
30. S. Abbas and M. Benchohra, On the generalized Ulam-Hyers-Rassias stability for Darboux problem for partial fractional implicit differential equations, Appl. Math. E-Notes 14 (2014), 20-28.
31. S. Abbas and M. Benchohra, Some stability concepts for Darboux problem for partial fractional differential equations on unbounded domain, Fixed Point Theory. (to appear).
32. S. Abbas, M. Benchohra and A. Cabada, Partial neutral functional integrodifferential equations of fractional order with delay, Bound. Value Prob. Vol. 2012 (2012), 128, 15 pp.
33. S. Abbas, M. Benchohra and T. Diagana, Existence and attractivity results for some fractional order partial integro-differential equations with delay, Afr. Diaspora J. Math. 15 (2) (2013), 87-100.
34. S. Abbas, M. Benchohra and L. Gorniewicz, Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative, Sci. Math. Jpn.. online e- 2010, 271-282.
35. S. Abbas, M. Benchohra and J. R. Graef, Integro-differential equations of fractional order, Differ. Equ. Dyn. Syst. 20 (2) (2012), 139-148.
36. S. Abbas, M. Benchohra and J. Henderson, Global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal. 19 (2012), 79-89.
37. S. Abbas, M. Benchohra and J. Henderson, Asymptotic behavior of solutions of nonlinear fractional order Riemann-Liouville Volterra-Stieltjes Quadratic integral equations, Int. Electron. J. Pure Appl. Math. 4 (3) (2012), 195-209.
38. S. Abbas, M. Benchohra and J.Henderson, Asumptotic attractive nonlinear fractional order Riemann-Liouville integral equations in Banach algebras, Nonlinear Stud. 20 (2013), 1-10.
39. S. Abbas, M. Benchohra and J. Henderson, Ulam stability for partial fractional integral inclusions via Picard operators, J. Frac. Calc. Appl., 5 (2)(2014), 133-144.
40. S. Abbas, M. Benchohra and G.M. N'Guérékata, Topics in Fractional Differential Equations, Developments in Mathematics, 27, Springer, New York, 2012.
41. S. Abbas, M. Benchohra and G.M. N'Guérékata, Asymptotic stability in nonlinear delay differential equations of fractional order, J. Nonlinear Evolution Equ. Appl. 2012, 85-96.
42. S. Abbas, M. Benchohra, G.M. N'Guérékata and B.A. Slimani, Darboux problem for fractional order discontinuous hyperbolic partial differential equations in Banach algebras, Complex Var. Elliptic Equ. 57 (2012), 337-350.
43. S. Abbas, M. Benchohra and J.J. Nieto, Global uniqueness results for fractional order partial hyperbolic functional differential equations, Adv. Difference Equ. 2011, Art. ID 379876, 25 pp.
44. S. Abbas, M. Benchohra and J.J. Nieto, Global attractivity of solutions for nonlinear fractional order Riemann-Liouville Volterra-Stieltjes partial integral equations, Electron. J. Qual. Theory Differ. Equ. 81 (2012), 1-15.
45. S. Abbas, M. Benchohra and J.J. Nieto, Functional implicit hyperbolic fractional order differential equations with delay, Afr. Diaspora J. Math. 15 (1) (2013), 74-96.
46. S. Abbas, M. Benchohra and J.J. Nieto, Ulam stabilities for impulsive partial fractional differential equations, Acta Univ. Palacki. Olomuc. 53 (1) (2014), 5-17.
47. S. Abbas, M. Benchohra, M. Rivero and J. J. Trujillo, Existence and stability results for nonlinear fractional order Riemann-LiouvilleVolterra-Stieltjes quadratic integral equations, submitted.
48. S. Abbas, M. Benchohra and S. Sivasundaram, Ulam stability for partial fractional differential inclusions with multiple delay and impulses via Picard operators, J. Nonlinear Stud. 20 (4) (2013), 623-641.
49. S. Abbas, M. Benchohra and J.J. Trujillo, Fractional order impulsive hyperbolic implicit differential equations with state-dependent delay, in Proceedings of the Sixth International Conference on Analytic Methods of Analysis and Differential Equations (AMADE-2011; Minsk, Belarus) [Dedicated to the Memory of Anatoly A. Kilbas] (Segei V. Rogosin, Editor), Publ. Center of the Belarusian State University, Minsk, Belarus, 2012, pp. 207-228 [ISBN 978-985-476-993-6].
50. S. Abbas, M. Benchohra and A. N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations, Frac. Calc. Appl. Anal. 15 (2) (2012), 168-182.
51. S. Abbas, M. Benchohra and Y. Zhou, Darboux problem for fractional order neutral functional partial hyperbolic differential equations, Int. J. Dyn. Syst. Differ. Equ. 2 (3&4) (2009), 301-312.
52. S. Abbas, M. Benchohra and Y. Zhou, Fractional order partial functional differential inclusions with infinite delay, Proc. A. Razmadze Math. Inst. 154 (2010), 1-19.
53. S. Abbas, M. Benchohra and Y. Zhou, Fractional order partial hyperbolic functional differential equations with state-dependent delay, Int. J. Dyn. Syst. Differ. Equ. 3 (4) (2011), 459-490.
54. N.H. Abel, Solutions de quelques problèmes à l'aide d'intégrales définies (1823). OEuvres complètes de Niels Henrik Abel, 1, Grondahl, Christiania, 1881, 11-18.
55. R. P. Agarwal, B. Andradec, G. Siracusa, On fractional integro-differential equations with state-dependent delay, Comput. Math. Appl. 63 (3) (2011), 1142-1149.
56. R.P Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential inclusions, Adv. Stud. Contemp. Math., 16 (2) (2008), 181-196.
57. R.P Agarwal, M. Benchohra and S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions,Acta. Appl. Math. 109 (2010), 973-1033.
58. R. P. Agarwal, M. Benchohra and B.A. Slimani, Existence results for differential equations with fractional order and impulses, Mem. Differential Equations Math. Phys. 44 (2008), 1-21.
59. R. P. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, Cambridge Tracts in Mathematics 141, Cambridge University Press, 2001.
60. R.P. Agarwal, D. O'Regan, S. Stanek, Positive solutions for Dirichlet problem of singular nonlinear fractional differential equations, J. Math. Anal. Appl. 371 (2010), 57-68.
61. R. P. Agarwal, D. O'Regan, M. A. Taoudi. Fixed point theorems for convex-power condensing operators relative to the weak topology and applications to Volterra integral equations. J. Integral Equations Appl. 24 (2012), 167-181.
62. R. P. Agarwal, D. O'Regan, M. A. Taoudi. Fixed point theorems for condensing multivalued mappings under weak topology features. Fixed Point Theory 12 (2011), 247-254.
63. R.P Agarwal, Y. Zhou and Y. He, Existence of fractional neutral functional differential equations, Comput. Math. Appl. 59 (3) (2010), 1095-1100.
64. R.P. Agarwal, Y. Zhou, J.Wang, X. Luo. Fractional functional differential equations with causal operators in Banach spaces. Math. Comput. Modelling 54 (2011), no. 5-6, 1440-1452.
65. O.P. Agrawal, O. Defterli, D. Baleanu. Fractional optimal control problems with several state and control variables. J. Vib. Control 16 (2010), no. 13, 1967-1976.
66. B. Ahmad, J.J. Nieto. Existence of solutions for impulsive anti-periodic boundary value problems of fractional order. Taiwanese J. Math. 15 (2011), no. 3, 981-993.
67. B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. Hybrid Syst. 3 (2009), 251-258.
68. E. Ait Dads, M. Benchohra and S. Hamani, Impulsive fractional differential inclusions involving the Caputo fractional derivative, Fract. Calc. Appl. Anal. 12 (1) (2009), 15-38.
69. R. Almeida, D.F.M. Torres, Fractional variational calculus for nondifferentiable functions. Comput. Math. Appl. 61 (2011), 3097-3104.
70. R. Almeida, D.F.M. Torres, Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives. Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1490-1500.
71. G. A. Anastassiou, Advances on Fractional Inequalities, Springer, New York, 2011.
72. D. Araya and C. Lizama, Almost automorphicmild solutions to fractional differential equations, Nonlinear Anal. 69 (2008), 3692-3705.
73. P. Arena, R. Caponetto, L. Fortuna, D. Porto, Nonlinear Noninteger Order Circuits and Systems. An Introduction.World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 38.World Scientific Publishing Co., Inc., River Edge, NJ, 2000. viii+203 pp.
74. O. Arino, S. Gautier, and J.P. Penot, A Fixed-point theorem for sequentially continuous mappings with application to ordinary differential equations, Funkc. Ekvac. 27 (1984), 273-279.
75. W. Arendt, C. Batty, M., Hieber, and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems,Monographs in Mathematics, 96 Birkhauser, Basel, 2001.
76. S. Arshad, V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal. 74 (2011), 3685-3693.
77. J. P. Aubin, Impulse differential inclusions and hybrid systems: a viability approach, Lecture Notes, Universit Paris-Dauphine, 2002.
78. J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, New York, 1984.
79. J.P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990.
80. K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive integrodifferetial equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 1970-1977.
81. K. Balachandran, J.J. Trujillo, The nonlocal Cauchy problemfor nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Anal. 72 (2010), 4587-4593.
82. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
83. D. Baleanu, S.I. Vacaru. Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics. J. Math. Phys. 52 (2011), no. 5, 053514, 15 pp.
84. J. Banás, Existence results for Volterra-Stieltjes quadratic integral equations on an unbounded interval, Math. Scand. 98(2006), 143-160.
85. J. Banás and B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal. 69 (7) (2008), 1945-1952.
86. J. Banàs and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
87. J. Banas and K. Sadarangani, Solvability of Volterra-Stieltjes operator-integral equations and their applications, Comput. Math. Appl. 41 (2001), 1535-1544.
88. J. Banás and T. Zajaç, A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl. 375 (2011), 375-387.
89. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leiden, 1976.
90. E. Bazhlekova, Fractional Evolution Equations in Banach Spaces, University Press Facilities, Eindhoven University of Technology, 2001.
91. A. Belarbi, M. Benchohra and A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal. 85 (2006), 1459-1470.
92. M. Benchohra, K. Ezzinbi and S. Litimein, Existence and controllability results for fractional order integro-differential inclusions in Fréchet spaces, Proc. A. Ramadze Math. Inst. 162 (2013), 1-23.
93. M. Benchohra, J. R. Graef and S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. Anal. 87 (7) (2008), 851-863.
94. M. Benchohra, J.R. Graef, F-Z. Mostefai. Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces. Electron. J. Qual. Theory Differ. Equ. 2010, No. 54, 10 pp.
95. M. Benchohra, J. Graef and F-Z. Mostefai, Weak solutions for boundary-value problems with nonlinear fractional differential inclusions, Nonlinear Dyn. Syst. Theory 11 (3) (2011), 227-237.
96. M. Benchohra, S. Hamani and S.K. Ntouyas, boundary value problems for differential equations with fractional order, Surv. Math. Appl. 3 (2008), 1-12.
97. M. Benchohra, J. Henderson and F-Z. Mostefai, Weak solutions for hyperbolic partial fractional differential inclusions in Banach spaces, Comput. Math. Appl. 64 (2012), 3101-3107.
98. M. Benchohra, J. Henderson and S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, Vol 2, New York, 2006.
99. M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for functional differential equations of fractional order, J. Math. Anal. Appl. 338 (2008), 1340-1350.
100. M. Benchohra and S. Litimein, A global uniqueness result for abstract integral equations of Volterra type in Banach spaces, Comm. Appl. Nonlinear Anal. 18 (1) (2011), 37-44.
101. M. Benchohra and S. Litimein, Fractional integro-differential equations with statedependent delay on an unbounded domain, Afr. Diaspora J. Math. 12 (2) (2011), 13-25.
102. M. Benchohra and S. Litimein, A global existence and uniqueness result for functional integro-differential equations in Banach spaces, An. Stiint,. Univ. Al. I. Cuza Iasi. Mat. (N.S.) LVIII (2012), 55-66.
103. M. Benchohra, S. Litimein and G. N'Guérékata, On fractional integro-differential inclusions with state-dependent delay in Banach spaces, Appl. Anal. 92 (2) (2013), 335-350.
104. M. Benchohra, S. Litimein, J. J. Trujillo and M.P. Velasco, Abstract fractional integro-differential equations with state-dependent delay, Intern. J. Evol. Equa. 6 (2) (2012), 25-38.
105. M. Benchohra and F-Z.Mostefai, Weak solutions for nonlinear differential equations with integral boundary conditions in Banach spaces, Opuscula Math. 32 (1) (2012), 31-40.
106. Benchohra and F-Z.Mostefai, Measure of weak noncompactness and fractional order Pettis integral equations with multiple time delay in Banach spaces, An. Stiint,. Univ. Al. I. Cuza Iasi. Mat. (N.S.) (to appear).
107. Benchohra, F-Z. Mostefai, J.J. Nieto and A. Ouahab, Weak solutions to boundary value problemof fractional order on unbounded domains in Banach spaces, Panamer. Math J. 23 (2013), 75-94.
108. M. Benchohra, J.J. Nieto, D. Seba. Measure of noncompactness and hyperbolic partial fractional differential equations in Banach spaces. Panamer. Math. J. 20 (2010), no. 3, 27-37.
109. M. Benchohra and S.K. Ntouyas, An existence theorem for an hyperbolic differential inclusion in Banach spaces. Discuss. Math. Differ. Incl. Control Optim. 22 (2002), 5-16.
110. M. Benchohra and S.K. Ntouyas, On an hyperbolic functional differential inclusion in Banach spaces. Fasc. Math. 33 (2002), 27-35.
111. M. Benchohra and S.K. Ntouyas, An existence result for hyperbolic functional differential inclusions. Comment. Math. Prace Mat. 42 (2002), 1-16.
112. M. Benchohra and B. A. Slimani, Existence and uniqueness of solutions to impulsive fractional differential equations, Electron. J. Differential Equations, Vol. 2009 (2009), No. 10, 11 pp.
113. A. Bica, V. A. Caus and S. Muresan, Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces, J. Inequal. Pure Appl. Math. 7, 5 (2006), Art. 173.
114. H.F. Bohnenblust and S. Karlin, On a theorem of ville. Contribution to the theory of games.155-160, Annals of Mathematics Studies, no. 24. Priceton University Press, Princeton. N. G. 1950.
115. M.F. Bota-Boriceanu, A. Petrusel, Ulam-Hyers stability for operatorial equations and inclusions, Analele Univ. I. Cuza Iasi 57 (2011), 65-74.
116. N. Bourbaki, Integration, Hermann, Paris, 1968, 2eme edition.
117. A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, StudiaMath. 90 (1988), 69-86.
118. D. Bugajewski, S. Szufla, Kneser's theorem for weak solutions of the Darboux problem in a Banach space, Nonlinear Anal. 20 (2) (1993), 169-173.
119. T.A. Burton, Fractional differential equations and Lyapunov functionals. Nonlinear Anal. 74 (2011), 5648-5662.
120. T. A. Burton, A fixed point theorem of Krasnoselskii, Appl. Math. Lett. 11 (1998), 85-88.
121. T. A. Burton. Volterra Integral and Differential Equations, Academic Press, New York, 1983.
122. T. A. Burton and T. Furumochi, Krasnosel'skii's fixed point theorem and stability, Nonlinear Anal. 49 (2002), 445-454.
123. T.A. Burton and C. Kirk, A fixed point theorem of Krasnoselskii-Schaefer type, Math. Nachr. 189 (1998), 23-31.
124. L.W. Busbridge, The Mathematics of Radiative Transfer, Cambridge Univ. Press, Cambridge, 1960.
125. x), J. Appl. Math. Stochastic Anal. 3 (1990), 163-168.
126. L. Byszewski, Theorem about existence and uniqueness of continuous solutions of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal., 40 (1991), 173-180.
127. L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional differential evolution nonlocal Cauchy problem, Selected Problems in Mathematics, Cracow Univ. of Tech. Monographs, Anniversary Issue 6 (1995), 25-33.
128. L. Byszewski and V. Lakshmikantam, Monotone iterative technique for non-local hyperbolic differential problem, J. Math. Phys. Sci 26 (1992), 345-359.
129. L. Byszewski and S. N. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem, J. Appl. Math. Stoch. Anal. 12 (1999), 179-180.
130. M. Caputo, Linear models of dissipation whose Q is almost frequency independent II. Geophys. J. Roy. Astron. Soc. 13, 529-539 (1967), reprinted in Fract. Calc. Appl. Anal. 11 (2008), 4-14.
131. M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geophys. J. R. Astr. Soc. 13 (1967), 529-539.
132. M. Caputo, Elasticit à e Dissipazione, Zanichelli, Bologna, 1969.
133. K.M. Case, P.F. Zweifel, Linear Transport Theory, Addison-Wesley, Reading, MA, 1967.
134. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
135. L.P. Castro, A. Ramos, Hyers-Ulam-Rassias stability for a class of Volterra integral equations, Banach J. Math. Anal. 3(2009), 36-43.
136. S. Chandrasekhar, Radiative Transfer, Oxford University Press, London, 1950.
137. Y.-K. Chang and J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions,Math. Comput. Model. 49 (2009), 605-609.
138. F. Chen, J.J. Nieto and Y. Zhou, Global attractivity for nonlinear fractional differential equations, Nonlinear Anal. Real World Appl. 13 (2012), 287-298.
139. T. Clarke, B. N. N. Achar, and J. W. Hanneken, Mittag-Leffler functions and transmission lines, J. Molecular Liquids 114 (1-3)(2004), 159-163.
140. C. Corduneanu, Integral Equations and Stability of Feedback Systems, Acedemic Press, New York, 1973.
141. C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.
142. H. Covitz and S. B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
143. T. Czlapinski, On the Darboux problem for partial differential-functional equations with infinite delay at derivatives. Nonlinear Anal. 44 (2001), 389-398.
144. T. Czlapinski, Existence of solutions of the Darboux problem for partial differentialfunctional equations with infinite delay in a Banach space. Comment. Math. Prace Mat. 35 (1995), 111-122.
145. M.F. Danca, K. Diethelm, Kai. Fractional-order attractors synthesis via parameter switchings. Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 12, 3745-3753.
146. M.A. Darwish, J. Henderson, D. O'Regan, Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument. Bull. Korean Math. Soc. 48 (2011), 539-553.
147. S. Das, Functional Fractional Calculus for System Identification and Controls, Springer-Verlag Berlin Heidelberg 2008.
148. S. Das, Functional Fractional Calculus, Springer-Verlag Berlin Heidelberg 2011.
149. xy 2 F(x, y, z) in Banach space, Ann. Soc. Math. Pol. Ser. I, Comment. Math., 30 (1) (1990), 41-49.
150. A. Debbouche. Fractional evolution integro-differential systems with nonlocal conditions. Adv. Dyn. Syst. Appl. 5 (2010), no. 1, 49-60.
151. A. Debbouche and D. Baleanu, Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems, Comput. Math. Appl. 62 (2011), 1442-1450.
152. F. S. De Blasi, G. Pianigiani and V. Staicu: On the solution sets of some nonconvex hyperbolic differential inclusions, Czechoslovak Math. J. 45 (1995), 107-116.
153. K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992.
154. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
155. D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609-625.
156. Z. Denton, A.S. Vatsala. Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Opuscula Math. 31 (2011), no. 3, 327-339.
157. B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Funct. Anal. Appl. 8 (2004), 563-575.
158. B. C. Dhage, Some algebraic fixed point theorems for multi-valued mappings with applications, Diss. Math. Differential Inclusions, Control & Optim. 26 (2006), 5-55.
159. B. C. Dhage, Nonlinear functional boundary value problems in Banach algebras involving Carathéodories, Kyungpook Mathematical Journal, 46 (4) (2006), 527-541.
160. B. C. Dhage, Existence theorems for hyperbolic differential inclusions in Banach algebras, J. Math. Anal. Appl. 335 (2007), 225-242.
161. B. C. Dhage, Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness, Diff. Equ. Appl. 2 (3) (2010), 299-318.
162. T. Diagana, G.M. Mophou and G.M. N'Guérékata, On the existence of mild solutions to some semilinear fractional integro-differential equations. Electron. J. Qual. Theory Differ. Equ. 2010, No. 58, 17 pp.
163. J. Diestel and J. J. Uhl Jr., Vector measures, in: Math. Surveys, 15, Amer. Math. Soc., Providence, R.I. 1977.
164. K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Springer, Berlin, 2010.
165. K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229-248.
166. K. Diethelm and A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in "Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties" (F. Keil, W. Mackens, H. Voss, and J. Werther, Eds), pp 217-224, Springer-Verlag, Heidelberg, 1999.
167. Y. Ding and H. He, A fractional-order differential equation model of HIV infection of CD4+ T-cells, Math. Comput. Modelling 50 (3-4) (2009), 386-392.
168. S. Djebali, D. O'Regan and Z. Sahnoun, Fixed point theorems for some operator equations and inclusions in Banach spaces relative to the weak topology, Commun. Appl. Anal. 16 (1) (2012), 1-10.
169. S. Djebali, D. O'Regan and Z. Sahnoun, On the solvability of some operator equations and inclusions in Banach spaces with the weak topology, Commun. Appl. Anal. 15 (1) (2011), 125-140.
170. X. Dong, J. Wang, Y. Zhou, Yong. On nonlocal problems for fractional differential equations in Banach spaces. OpusculaMath. 31 (2011), no. 3, 341-357.
171. S. Dugowson, L'élaboration par Riemann d'une définition de la dérivation d'ordre non entier, revue d'histoire des Mathématiques 3 (1997), 49-97.
172. G. A. Edgar, Geometry and the Pettis-integral, Indiana Univ. Math. J. 26 (1977), 663-677.
173. G. A. Edgar, Geometry and the Pettis-integral II, Indiana Univ. Math. J. 28 (1979), 559-579.
174. M. M. El-Borai and A. Debbouche, On some fractional integro-differential equations with analytic semigroups, Interna. J. ContemporaryMath. Sci. 4 (2009), 1361-1371.
175. M. M. El-Borai, On some fractional evolution equations with nonlocal conditions. Int. J. Pure Appl. Math. 24 (2005), 405-413.
176. M. M. El-Borai, The fundamental solutions for fractional evolution equations of parabolic type. J. Appl. Math. Stoch. Anal. 2004 (3), 197-211.
177. M.M. El-Borai, K. El-Said El-Nadi, E.G. El-Akabawy On some fractional evolution equations. Comput. Math. Appl. 59 (2010), no. 3, 1352-1355.
178. M.M. El-Borai, K. El-Nadi, H.A. Fouad. On some fractional stochastic delay differential equations. Comput. Math. Appl. 59 (2010), no. 3, 1165-1170.
179. A. M. A. El-Sayed, Fractional order evolution equations, J. Fract. Calc. 7 (1995), 89-100.
180. A. M. A. El-Sayed, Fractional order diffusion-wave equations, Intern. J. Theo. Physics 35 (1996), 311-322.
181. A. M. A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998), 181-186.
182. A. M. A. El-Sayed, A. E. M. El-Mesiry, H. A. A. El-Saka, On the fractional-order logistic equation, Appl. Math. Lett. 20 (7) (2007), 817-823.
183. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.
184. H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland, Mathematical Studies, 108, North-Holland, Amsterdam, 1985.
185. J.B.J. Fourier, Théorie Analytique de la Chaleur, Didot, Paris (1822), 499-508.
186. M. Frigon, Théorèmes d'existence de solutions d'inclusions différentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol. 472, Kluwer Academic Publishers, Dordrecht, 1995, 51-87.
187. M. Frigon and A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité, C. R. Acad. Sci. Paris, Ser. I 310 (1990), 819-822.
188. M. Frigon and D. O'Regan, Impulsive differential equations with variable times, Nonlinear Anal. 26 (1996), 1913-1922.
189. M. Frigon and D. O'Regan, First order impulsive initial and periodic problems with variable moments, J. Math. Anal. Appl. 233 (1999), 730-739.
190. M. Frigon and D. O'Regan, Second order Sturm-Liouville BVP's with impulses at variable moments, Dynam. Contin. Discrete Impuls. Systems 8 (2), (2001), 149-159.
191. K. M. Furati and N.-eddine Tatar, Behavior of solutions for a weighted Cauchy-type fractional differential problem, J. Frac. Calc. 28 (2005), 23-42.
192. K. M. Furati and N.-eddine Tatar, Power type estimates for a nonlinear fractional differential equation, Nonlinear Anal. 62 (2005), 1025-1036.
193. L. Gaul, P. Klein and S. Kempfle, Damping description involving fractional operators, Mech. Systems Signal Processing 5 (1991), 81-88.
194. R. F. Geitz, Pettis integration, Proc Amer. Math. Soc 82 (1981), 81-86.
195. R. F. Geitz, Geometry and the Pettis integration, Trans. Amer.Math. Soc. 269 (1982), 535-548.
196. W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of selfsimilar protein dynamics, Biophys. J. 68 (1995), 46-53.
197. W. G. Glóckle and T. F. Nonnenmacher, Fractional integral operators and Fox functions in the theory of viscoelasticity.Macromolecules, 24 (1991) 64266434.
198. R. Gorenflo and F. Mainardi, Some recent advances in theory and simulation of fractional diffusion processes, J. Comput. Appl. Math. 229 (2) (2009), 400-415.
199. R. Gorenflo and F. Mainardi, Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects, Chap. 4 In R. Klages, G. Radons and I.M. Sokolov (Editors): Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim, Germany, 2008, pp. 93-127.
200. R. Gorenflo, F.Mainardi and A. Vivoli, Continuous time randomwalk and parametric subordination in fractional diffusion, Chaos, Solitons Fractals 34 (2007), 87-103.
201. R. Gorenflo and S. Vessella, Abel Integral Equations, Lecture Notes in Math., 1461, Springer, Berlin, 1991.
202. L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
203. N. M. Grahovac, Modelling of the hamstring muscle group by use of fractional derivatives. Comput. Math. Appl., 59 (2010), 1695-1700.
204. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
205. A.K. Grunwald, Dérivationen und deren Anwendung, Zeitschrift für Mathematik und Phisik, 12 (1867), 441-480.
206. D.J. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht, 1996.
207. J. Hale and J. Kato, Phase space for retarded equationswith infinite delay, Funkcial. Ekvac. 21, (1978),11-41.
208. J. K. Hale and S. Verduyn Lunel, Introduction to Functional -Differential Equations, Applied Mathematical Sciences, 99, Springer-Verlag, New York, 1993.
209. F. Hartung, Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays, J. Math. Anal. Appl. 324 (1) (2006), 504-524.
210. F. Hartung, Linearized stability in periodic functional differential equations with state-dependent delays, J. Comput. Appl. Math. 174 (2) (2005), 201-211
211. S.W. Hawking, A Brief History of Time, Bantam Press, London (1988).
212. D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer-Verlag, Berlin/New York, 1989.
213. S. Heikkila and V. Lakshmikantham, Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations, Marcel Dekker Inc., New York, 1994.
214. D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer-Verlag, Berlin/New York, 1989.
215. J. Henderson and A. Ouahab, Fractional functional differential inclusions with finite delay, Nonlinear Anal. 70 (2009), 2091-2105.
216. J. Henderson, A. Ouahab, Impulsive differential inclusions with fractional order, Comput. Math. Appl. 59 (2010), 1191-1226.
217. J. Henderson, A. Ouahab, A Filippov's theorem, some existence results and the compactness of solution sets of impulsive fractional order differential inclusions. Mediterr. J. Math. 9 (2012), 453-485.
218. J. Henderson and C. Tisdell, Topological transversality and boundary value problems on time scales, J. Math. Anal. Appl. 289 (2004), 110-125.
219. E. Hernández, A. Prokopczyk and L. Ladeira, Anote on partial functional differential equations with state-dependent delay. Nonlinear Anal. Real World Applications 7 (2006), 510-519.
220. E. HernandezM., R. Sakthivel, S. Tanaka Aki, Existence results for impulsive evolution differential equations with state-dependent delay, Electron. J. Differential Equations 2008 (2008), No. 28 pp. 1-11.
221. M.A.E. Herzallah, D. Baleanu, Fractional-order variational calculus with generalized boundary conditions. Adv. Difference Equ. 2011, Article ID 357580, 9 p.
222. M.A.E. Herzallah, A.M.A. El-Sayed, D. Baleanu. Perturbation for fractional-order evolution equation. Nonlinear Dynam. 62 (2010), no. 3, 593-600.
223. N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 45 (5) (2006), 765-772.
224. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
225. E. Hille and R. S. Phillips, Functional analysis and semi-groups, in: Amer. Math. Soc. Colloq., Publ. 31, Amer. Math. Soc., Providence, RI, 1957.
226. Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, in: Lecture Notes in Mathematics, 1473, Springer-Verlag, Berlin, 1991.
227. S. Hu, M. Khavanin and W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), 261-266.
228. Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory I, Kluwer, Dordrecht, 1997.
229. D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224.
230. D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhuser, 1998.
231. R.W. Ibrahim, Existence and uniqueness of holomorphic solutions for fractional Cauchy problem. J. Math. Anal. Appl. 380 (2011), 232-240.
232. R.W. Ibrahimand H.A. Jalab, Existence of the solution of fractiona integral inclusion with time delay, Misk. Math. Notes 11 (2) (2010), 139-150.
233. B.N. Ivanov, Printsipy Sovremennoi Fziki (Principles of Modern Physics). Nauka, Moscow (1973) (In Russian).
234. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
235. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, 2011.
236. S.-M. Jung, A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl. 2007 (2007), Article ID 57064, 9 pages.
237. T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, 2011.
238. A. Kadem, D. Baleanu. Homotopy perturbation method for the coupled fractional Lotka-Volterra equations. Romanian J. Phys. 56 (2011), no. 3-4, 332-338.
239. Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications. Kluwer Academic Publishers, Dordrecht, 1999.
240. Z. Kamont, and K. Kropielnicka, Differential difference inequalities related to hyperbolic functional differential systems and applications. Math. Inequal. Appl. 8 (4) (2005), 655-674.
241. E.R. Kaufmann and E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 2007, No. 3, 11 pp.
242. A. A. Kilbas, B. Bonilla and J. Trujillo, Nonlinear differential equations of fractional order in a space of integrable functions, Dokl. Ross. Akad. Nauk, 374 (4) (2000), 445-449.
243. A. A. Kilbas and S. A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuouslydifferentiable functions,Differential Equations 41 (2005), 84-89.
244. A. A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations.North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
245. M. Kirane, M. Medved, N. Tatar. Semilinear Volterra integrodifferential problems with fractional derivatives in the nonlinearities. Abstr. Appl. Anal. 2011, Art. ID 510314, 11 pp.
246. V.S. Kiryakova, Y.F. Luchko. The multi-index Mittag-Leffler functions and their appplications for solving fractional order problems in applied analysis. Application of mathematics in technical and natural sciences, 597-613, AIP Conf. Proc., 1301, Amer. Inst. Phys., Melville, NY, 2010.
247. M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
248. J. Klafter, S. C. Lim, R. Metzler, Fractional Dynamics in Physics: Recent Advances, World Scientific, Singapore 2011.
249. R.C. Koeller, Application of fractional calculus to the theory of viscoelasticity, J. Appl. Mechanics 51, (1984), 299307.
250. S. Labidi, N. Tatar. Blow-up of solutions for a nonlinear beam equation with fractional feedback. Nonlinear Anal. 74 (2011), no. 4, 1402-1409.
251. S.F. Lacroix, Traité du Calcul Différentiel et du Calcul Intégral, Courcier, Paris, t.3 (1819), 409-410.
252. G.S. Ladde, V. Lakshmikanthan and A. S. Vatsala, Monotone Iterative Techniques for Nonliner Differential Equations, Pitman Advanced Publishing Program, London, 1985.
253. V. Lakshmikantham, Theory of fractional differential equations, Nonlinear Anal. 60 (2008), 3337- 3343.
254. V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of FractionalDynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
255. V. Lakshmikantham and S. G. Pandit, The method of upper, lower solutions and hyperbolic partial differential equations, J. Math. Anal. Appl. 105 (1985), 466-477.
256. V. Lakshmikantham, N.S. Papageorgiou, and J. Vasundhara, The method of upper and lower solutions and monotone technique for impulsive differential equations with variable moments, Appl. Anal. 15 (1993), 41-58.
257. V. Lakshmikantham and A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (2008), 2677-2682.
258. V. Lakshmikantham, L. Wen and B. Zhang, Theory of Differential Equations with Unbounded Delay, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 1994.
259. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
260. G.W. Leibniz, Letter from Hanover, Germany, Deptember 30, 1695 to G.A. L'Hospital, JLeibnizen Mathematische Schriften 2, 301-302. Olms Verlag, Hildesheim, Germany, (1962). First published in 1849.
261. F. Li and G.M. N'Guérékata, An existence result for neutral delay integrodifferential equations with fractional order and nonlocal conditions. Abst. Appl. Anal. (2011), Article ID 952782, 20 pages.
262. Y. Li, Y. Chen, I. Podlubny, Igor. Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59 (2010), no. 5, 1810-1821.
263. V. Libertiaux and F. Pascon, Differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissuemodeling. J. Comput. Appl.Math., 234 (2010), 2029-2035.
264. T.C. Lim, On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J. Math. Anal. Appl. 110 (1985), 436-441.
265. J. Liouville, Mémoire sur le calcul des différentielles à indices quelconques, J. l'Ecole Roy. Polytéchn. 13 (1832), 529-539.
266. C. Lizama, Regularized solutions for abstract Volterra equations, J.Math. Anal. Appl. 243 (2000), 278-292.
267. C. Lizama and J. Sánchez, On perturbation of k-regularized resolvent families, Taiwan. J. Math. 7, (2003), 217-227.
268. Y. Luchko, Initial-boundary-value problems for the generalized multi-term timefractional diffusion equation. J. Math. Anal. Appl. 374 (2011), 538-548.
269. R. Magin, Fractional Calculus in Bioengineering. Begell House Publishers, Redding, 2006.
270. R. Magin, M.D. Ortigueira, I. Podlubny, J.J. Trujillo, On the fractional signals and systems. Signal Process 91 (2011), 350-371.
271. F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in "Fractals and Fractional Calculus in Continuum Mechanics " (A. Carpinteri and F. Mainardi, Eds), pp. 291-348, Springer-Verlag, Wien, 1997.
272. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to MathematicalModels, Imperial College Press, London 2010.
273. F. Mainardi, G. Pagnini and R. Gorenflo, Some aspects of fractional diffusion equations of single and distributed order, Appl. Math. Comput. 187 (2007), 295-305.
274. S. Marano and V. Staicu, On the set of solutions to a class of nonconvex nonclosed differential inclusions, Acta Math. Hungar. 76 (1997), 287-301.
275. F. Metzler, W. Schick, H. G. Kilian and T. F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys. 103 (1995), 7180-7186.
276. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, JohnWiley & Sons, New York, 1993.
277. A.R. Mitchell, Ch. Smith, An existence theorem for weak solutions of differential equations in Banach spaces in: V. Lakshmikantham (Ed.), Nonlinear Equations in Abstract Spaces, 1978, pp. 387-404.
278. α, C. R. Acad. Sci. Paris, 137 (1903), 554-558.
279. α(x), Rend. Accad. Lincei, ser. 5, 13 (1904), 3-5.
280. y, J. Korean Math. Soc., 41 (2004), 995-1005.
281. K. Moaddy, S. Momani, I. Hashim. The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. Comput. Math. Appl. 61 (2011), no. 4, 1209-1216.
282. G.M. Mophou, Optimal control of fractional diffusion equation. Comput. Math. Appl. 61 (2011), 68-78.
283. M. Mophou, O. Nakoulima and G. M. N'Guérékata, Existence results for some fractional differential equations with nonlocal conditions, Nonlinear Stud. 17 (2010), 15-22.
284. G.M. Mophou and G.M. N'Guérékata, Existence of the mild solution for some fractional differential equations with nonlocal conditions. Semigroup Forum 79 (2009), 315-322.
285. G. M. Mophou, G.M. N'Guérékata, On some classes of almost automorphic functions and applications to fractional differential equations, Comput. Math. Appl. 59 (2010), 1310-1317.
286. G.M. Mophou and G.M. N'Guérékata, On integral solutions of some nonlocal fractional differential equations with nondense domain. Nonlinear Anal. 71 (2009), 4668-4675.
287. G.M. Mophou, G.N. N'Guérékata, Controllability of semilinear neutral fractional functional evolution equations with infinite delay. Nonlinear Stud. 18 (2011), 195-209.
288. G. M. Mophou, G.M. N'Guérékata and V. Valmorin. Pseudo almost automorphic solutions of a neutral functional fractional differential equations. Intern. J. Evol. Equ. 4 (2009), 129-139.
289. A. Mura and F. Mainardi, A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics, Integral Transforms Special Funct. 20 (3-4)(2009), 185-198.
290. V. Mureşan, Functional-integral equations, Ed. Mediamira, Cluj-Napoca, 2003.
291. V. Mureşan, Some results on the solutions of a functional-integral equation Stud. Univ. Babes-BolyaiMath. 56 (2011), 157-164.
292. S. Muslih, O.P. Agrawal. Riesz fractional derivatives and fractional dimensional space. Internat. J. Theoret. Phys. 49 (2010), no. 2, 270-275.
293. S. Muslih, O. P. Agrawal, D. Baleanu. A fractional Schrödinger equation and its solution. Internat. J. Theoret. Phys. 49 (2010), no. 8, 1746-1752.
294. I. P. Natanson, Theory of Functions of a Real Variable, Ungar, New York, 1960.
295. J.J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Appl. Math. Lett., 23 (2010), 1248-1251.
296. K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974.
297. D. O'Regan, Fixed point theory for weakly sequentially continuous mapping, Math. Comput. Model. 27 (5) (1998), 1-14.
298. D. O'Regan, Weak solutions of ordinary differential equations in Banach spaces, Appl. Math. Lett. 12 (1999), 101-105.
299. D. O'Regan, M.-A. Taoudi. Fixed point theorems for the sum of two weakly sequentially continuous mappings. Nonlinear Anal. 73 (2010), 283-289.
300. M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Springer-Verlag, Dordrecht, 2011.
301. A. Ouahab. Fractional semilinear differential inclusions. Comput. Math. Appl. 64 (2012), 3235-3252.
302. B. G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstratio Math. XL (4) (2007), 839-852.
303. B. G. Pachpatte, On Fredholm type integrodifferential equation, Tamkang J. Math. 39 (2008), 85-94.
304. B.G. Pachpatte, On Fredholm type integral equation in two variables Diff. Equ. Appl. 1 (2009), 27-39.
305. B. G. Pachpatte, On a general partial integral equation of Barbashin type,Tamsui Oxford J. Math. Sci. 27 (2011), 99-115.
306. S. G. Pandit, Monotone methods for systems of nonlinear hyperbolic problems in two independent variables, Nonlinear Anal., 30 (1997), 235-272.
307. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
308. T.P. Petru, and M.-F. Bota, Ulam-Hyers stabillity of operational inclusions in complete gauge spaces, Fixed Point Theory 13 (2012), 641-650.
309. T.P. Petru, A. Petrusel. J.-C. Yao, Ulam-Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese J. Math. 15 (2011), 2169-2193.
310. L. M. Petrovic, and T. M. Atanackovic, A model for shrinkage strain in photo polymerization of dental composites, Dental Materials 24 (4) (2008), 556-560.
311. L. M. Petrovic, D. T. Spasic, and T. M. Atanackovic, On a mathematical model of a human root dentin, Dental Materials 21 (2) (2005), 125-128.
312. B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), 277-304.
313. R.S. Phillips, A decomposition of additive set functions, Bull. Amer. Math. Soc. 46 (1940), 274-277.
314. I. Podlubny, Fractional Differential Equations,Mathematics in science and engineering 198, Academic Press, San Diego, 1999.
315. I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calculus Appl. Anal. 5 (2002), 367-386.
316. I. Podlubny, I. Petraš, B. M. Vinagre, P. O'Leary and L. Dorčak, Analogue realizations of fractional-order controllers. Fractional order calculus and its applications, Nonlinear Dynam. 29 (2002), 281-296.
317. Y. Z. Povstenko, Fractional radial diffusion in a cylinder. J. Molecular Liquids 137 (1-3) (2008), 46-50.
318. J. Prüss, Evolutionary Integral Equations and Applications Monographs Math. 87, Bikhäuser Verlag, 1993.
319. C. Qian, Global attractivity in nonlinear delay differential equations, J. Math. Anal. Appl. 197 (1996), 529-547.
320. C. Qian, Global attractivity in a delay differential equation with application in a commodity model, Appl. Math. Lett. 24 (2011), 116-121.
321. C. Qian, Global attractivity in a nonlinear delay differential equation with applications. Nonlinear Anal. 71 (2009), 1893-1900.
322. M.D. Quinn and N. Carmichael, An approach to nonlinear control problem using fixed point methods, degre theory, pseudo-inverse,Numer. Funct. Anal. Optim., 7 (1984-85), 197-219.
323. Th.M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
324. J.D. Ramirez, A.S. Vatsala. Monotone method for nonlinear Caputo fractional boundary value problems. Dynam. Systems Appl. 20 (2011), no. 1, 73-88.
325. A. Razminia, V.J. Majd, D. Baleanu. Chaotic incommensurate fractional order Rössler system: active control and synchronization. Adv. Difference Equ. 2011, 2011:15, 12 pp.
326. M. Rivero, J.J. Trujillo, L. Vazquez, M.P. Velasco. Fractional dynamics of populations. Appl. Math. Comput. 218 (2011), 1089-1095.
327. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1970.
328. I. A. Rus, Ulam stability of ordinary differential equations, Studia Univ. Babes-Bolyai, Math. LIV (4)(2009), 125-133.
329. I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory 10 (2009), 305-320.
330. J. Sabatier, O. Agrawal, J. Machado (Eds.), Advances in Fractional Calculus. Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht, 2007.
331. J. Sabatier, M. Merveillaut, R. Malti, A. Oustaloup. How to impose physically coherent initial conditions to a fractional system? Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 5, 1318-1326.
332. H.A.H. Salem, On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies, Comput. Math. Appl. 224 (2009), 565-572.
333. H.A.H. Salem. On the fractional calculus in abstract spaces and their applications to the Dirichlet-type problem of fractional order. Comput. Math. Appl. 59 (2010), no. 3, 1278-1293.
334. H.A.H. Salem. Global monotonic solutions of multi term fractional differential equations. Appl. Math. Comput. 217 (2011), no. 14, 6597-6603.
335. H. A. H. Salem, A. M. A. El-Sayed and O. L. Moustafa, A note on the fractional calculus in Banach spaces, Studia Sci. Math. Hungar. 42 (2) (2005), 115-130.
336. H. A. H. Salem and M. Väth, An abstract Gronwall lemma and applications to global existence results for functional differential and integrals of fractional order, J. Integral Equations Appl. 16 (2004), 411-439.
337. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
338. N. Samko, S. Samko, B. Vakulov. Fractional integrals and hypersingular integrals in variable order Hlder spaces on homogeneous spaces. J. Funct. Spaces Appl. 8 (2010), no. 3, 215-244.
339. N. P. Semenchuk, On one class of differential equations of noninteger order, Differents. Uravn., 10 (1982), 1831-1833.
340. H. Sheng, Y. Chen, T. Qiu, Fractional Processes and Fractional-order Signal Processing; Techniques and Applications. Springer-Verlag, 2011.
341. Jong Son Shin, An existence theoremof functional differential equations with infinite delay in a Banach space, Funkcial. Ekvac. 30 (1987), 19-29.
342. X. Su and S. Zhang, Unbounded solutions to a boundary value problem of fractional order on the half-line, Comput. Math. Appl. 61 (2011), 1079-1087.
343. M.-A. Taoudi. Krasnoselskii type fixed point theorems underweak topology features. Nonlinear Anal. 72 (2010), 478-482.
344. V. E. Tarasov, Fractional dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg; Higher Education Press, Beijing, 2010.
345. V. E. Tarasov. Fractional dynamics of relativistic particle. Internat. J. Theoret. Phys. 49 (2010), no. 2, 293-303.
346. V. E. Tarasov. M. Edelman. Fractional dissipative standard map. Chaos 20 (2010), no. 2, 023127, 7 pp.
347. J.A. Tenreiro Machado. Time-delay and fractional derivatives. Adv. Difference Equ. 2011, Art. ID 934094, 12 pp.
348. J.A. Tenreiro Machado. Entropy analysis of integer and fractional dynamical systems. Nonlinear Dynam. 62 (2010), no. 1-2, 371-378.
349. J.A. Tenreiro Machado Time-delay and fractional derivatives. Adv. Difference Equ. 2011, Art. ID 934094, 12 pp.
350. J.A. Tenreiro Machado, Time-delay and fractional derivatives. Adv. Difference Equ. 2011, Article ID 934094, 12 p.
351. J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi. A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13 (2010), no. 4, 447-454.
352. J.A. Tenreiro Machado, V. Kiryakova, F. Mainardi. Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 3, 1140-1153.
353. J.C. Trigeassou, N. Maamri, J. Sabatier, A.A. Oustaloup, Lyapunov approach to the stability of fractional differential equations. Signal Process 91 (2011), 437-445.
354. V. V. Uchaikin, FractionalDerivatives for Physicists and Engineers.Volume I. Background and theory. Nonlinear Physical Science. Higher Education Press, Beijing; Springer, Heidelberg, 2013.
355. V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers. Volume II. Applications. Nonlinear Physical Science. Higher Education Press, Beijing; Springer, Heidelberg, 2013.
356. S.M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1968.
357. L. Vazquez. From Newton's equation to fractional diffusion and wave equations.Adv. Difference Equ. 2011, Art. ID 169421, 13 pp.
358. A. N. Vityuk, On solutions of hyperbolic differential inclusions with a nonconvex right-hand side. (Russian) Ukran. Mat. Zh. 47 (1995), no. 4, 531-534; translation in Ukrainian Math. J. 47 (1995), no. 4, 617-621 (1996).
359. A. N. Vityuk, Existence of Solutions of partial differential inclusions of fractional order, Izv. Vyssh. Uchebn., Ser. Mat., 8 (1997), 13-19.
360. A. N. Vityuk and A. V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil. 7 (3) (2004), 318-325.
361. A. N. Vityuk and A. V. Golushkov, The Darboux problem for a differential equation containing a fractional derivative, Nonlinear Oscil. 8 (2005), 450-462.
362. A. N. Vityuk and A. V. Mykhailenko, On one class of differential quations of fractional order, Nonlinear Oscil. 11 (3) (2008), 307-319.
363. A. N. Vityuk and A. V. Mykhailenko, The Darboux problem for an implicit fractional-order differential equation, J. Math. Sci. 175 (4) (2011), 391-401.
364. J. Wang, Y. Zhou and M. Fečkan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl. 64 (2012), 3389-3405.
365. J. Wang, Y. Zhou, W. Wei. A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 10, 4049-4059.
366. J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, E. J. Qual. Theory Diff. Equ. (63) (2011) 1-10.
367. J. Wang, L. Lv, Y. Zhou, New concepts and results in stability of fractional differential equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 2530-2538.
368. W. Wei, X. Li, X. Li, New stability results for fractional integral equation, Comput. Math. Appl. 64 (2012), 3468-3476.
369. S. Westerlund, Dead Matter has Memory! Causal Consulting, Kalmar, Sweden (2002).
370. T.-J. Xiao, J. Liang, and J. van Casteren, Time dependent Desch-Schappacher type perturbations of Volterra integral equations, Integral Equations Operator Theory 44 (4) (2002), 494-506.
371. th edn. Springer-Verlag, Berlin, 1980.
372. C. Yu and G. Gao, Existence of fractional differential equations, J. Math. Anal. Appl. 310 (2005), 26-29.
373. P.P. Zabrejko, A.I. Koshelev, M.A. Krasnosel'skii, S.G. Mikhlin, L.S. Rakovschik and V.J. Stecsenko, Integral Equations, Noordhoff, Leyden, 1976.
374. G. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, New York, 2005.
375. S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional diffrential equations, Electron. J. Differential Equations 2006, No. 36, pp. 1-12.
376. S. Zhang, Existence of positive solutions of a singular partial differential equation, Math. Bohemica 133 (1) (2008), 29-40.
377. Y. Zhou, Existence and uniqueness of fractional functional differential equations with unbounded delay. Int. J. Dyn. Syst. Differ. Equ. 1 (4) (2008), 239-244.
378. Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
379. Y. Zhou, F. Jiao and J. Li, Existence and uniqueness for p-type fractional neutral differential equations. Nonlinear Anal. 71 (2009), 2724-2733.
380. Y. Zhou, F. Jiao and J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71 (2009), 3249-3256.