Fractional semilinear differential inclusions

Computers and Mathematics with Applications

Volumn 64, Issue 10, 2012, Pages 3235-3252

  Ouahab, Abdelghani ^a  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

Author keywords

Absolute retract; Compactness; Fixed point; Fractional derivative; Fractional differential inclusions; Fractional integral

Indexed keywords

ABSOLUTE RETRACT; COMPACTNESS; FIXED POINTS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL INCLUSIONS; FRACTIONAL INTEGRALS;

DIFFERENTIATION (CALCULUS);

DIFFERENTIAL EQUATIONS;

EID: 84868208258     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.03.039     Document Type: Article

References (48)

1. K. Diethelm, and A.D. Freed On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity F. Keil, W. Mackens, H. Voss, J. Werther, Scientific Computing in Chemical Engineering II - Computational Fluid Dynamics, Reaction Engineering and Molecular Properties 1999 Springer-Verlag Heidelberg 217 224
2. L. Gaul, P. Klein, and S. Kempfle Damping description involving fractional operators Mech. Systems Signal Processing 5 1991 81 88
3. W.G. Glockle, and T.F. Nonnenmacher A fractional calculus approach of self-similar protein dynamics Biophys. J. 68 1995 46 53
4. F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanis A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer-Verlag Wien 291 348
5. 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
6. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematics Studies vol. 204 2006 Elsevier Science B. V Amsterdam
7. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley New York
8. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
9. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives, Theory and Applications 1993 Gordon and Breach Yverdon
10. K. Diethelm, and N.J. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
11. A.M.A. El-Sayed Nonlinear functional differential equations of arbitrary orders Nonlinear Anal. 33 1998 181 186 (Pubitemid 128403304)
12. A.A. Kilbas, and J.J. Trujillo Differential equations of fractional order: methods, results and problems II Appl. Anal. 81 2002 435 493
13. A.M. Nakhushev The Sturm-Liouville problems for a second order ordinary equations with fractional derivatives in the lower Dokl. Akad. Nauk SSSR 234 1977 308 311
14. M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 2008 1340 1350
15. V. Lakhmikantham Theory of fractional functional differential equations Nonlinear Anal. 69 2008 3337 3343
16. V. Lakshmikantham, and A.S. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
17. A. Aghajani, J. Banaś, and Yaghoub Jalilian Existence of solutions for a class of nonlinear Volterra singular integral equations Comput. Math. Appl. 62 2011 1215 1227
18. M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional functional differential inclusions with infinite delay and application to control theory Fract. Calc. Appl. Anal. 11 2008 35 56
19. J. Henderson, and A. Ouahab Fractional functional differential inclusions with finite delay Nonlinear Anal. 70 2009 2091 2105
20. J. Henderson, and A. Ouahab Impulsive differential inclusions with fractional order Comput. Math. Appl. 59 2010 1191 1226
21. F. Jiao, and Y. Zhou Existence of solutions for a class of fractional boundary value problems via critical point theory Comput. Math. Appl. 62 2011 1181 1199
22. A. Ouahab Some results for fractional boundary value problem of differential inclusions Nonlinear Anal. 69 2008 3877 3896
23. A. Ouahab Filippov's theorem for impulsive differential inclusions with fractional order Electron. J. Qual. Theory Differ. Equ. 23 2009 23 Spec, Ed. I
24. K. Deimling Multivalued Differential Equations 1992 Walter De Gruyter Berlin, New York
25. J.P. Aubin, and H. Frankowska Set-Valued Analysis 1990 Birkhäuser Boston
26. L. Górniewicz Topological Fixed Point Theory of Multivalued Mappings Mathematics and Its Applications vol. 495 1999 Kluwer Dordrecht
27. Q.J. Zhu On the solution set of differential inclusions in Banach Space J. Differential Equations 93 1991 213 237
28. 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
29. M. Kamenskii, V. Obukhovskii, and P. Zecca Condensing Multi-valued Maps and Semilinear Differential Inclusions in Banach Spaces 2001 de Gruyter Berlin
30. R.R. Akhmerov, M.I. Kamenskij, A.S. Potapov, A.E. Rodkina, and B.N. Sadovskij Measures of Noncompactness and Condensing Operators 1986 Nauka Novosibirsk (in Russian). Engl. transl.: Birkhäuser, Basel 1992
31. J.M.A. Toledano, T.D. Benavides, and G.L. Azedo Measures of Noncompactness in Metric Fixed Point Theory 1997 Birkhauser Basel
32. Sh. Hu, and N. Papageorgiou Handbook of Multivalued Analysis, Volume I: Theory 1997 Kluwer Dordrecht, Boston, London
33. M. Kisielewicz Differential Inclusions and Optimal Control 1991 Kluwer Dordrecht, The Netherlands
34. A.A. Tolstonogov Differential Inclusions in a Banach Space 2000 Kluwer Dordrecht, The Netherlands
35. M. Caputo Elasticità e Dissipazione 1969 Zanichelli Bologna
36. M. Caputo Linear models of dissipation whose Q is almost frequency independent, part II Geophys. J. R. Astr. Soc. 13 1967 529 539
37. M. Captuo, and F. Mainardi Linear models of dissipation in inelastic solids Riv. Nuovo Cimento (Ser. II) 1 1971 161 198
38. S.G. Krein Linear Differential Equations in Banach Space 1963 Nauka Moskow English translation: Transl. of Math. Monographs, vol. 29, Amer. Math. Soc., Providence, 1971
39. H. Markus The Functional Calculus for Sectorial Operators Oper. Theory Adv. Appl. vol. 69 2006 Birkhäuser-Verlag Basel
40. F. Periago, and B. Straub A functional calculus for almost sectorial operators and applications to abstract evolution equations J. Evol. Equ. 2 2002 41 68 (Pubitemid 135713586)
41. R.N. Wang, D.H. Chena, and T.J. Xiao Abstract fractional Cauchy problems with almost sectorial operators J. Differential Equations 252 2012 202 235
42. C. Castaing, and M. Valadier Convex Analysis and Measurable Multifunctions Lecture Notes in Mathematics vol. 580 1977 Springer-Verlag Berlin, Heidelberg, New York
43. H. Covitz, and S.B. Nadler Jr. Multivalued contraction mappings in generalized metric spaces Israel J. Math. 8 1970 5 11
44. B. Ricceri Une propriété topologique de l'ensemble des points fixe d'une contraction moultivoque à valeurs convexes Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 1987 283 286
45. R.E. Megginson An Introduction to Banach Space Theory Graduate Texts in Math. vol. 183 1998 Springer Verlag New York
46. S. Djebali, L. Górniewicz, and A. Ouahab Filippov's theorem and solution sets for first order impulsive semilinear functional differential inclusions Topol. Methods Nonlinear Anal. 32 2008 261 312
47. C. Gori, V. Obukhovskii, M. Ragni, and P. Rubbioni Existence and continuous dependence results for semilinear functional differential inclusions with infinite delay Nonlinear Anal. TMA 51 2002 765 782 (Pubitemid 34862821)
48. J.M.A.M. van Neerven, and B. Straub On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent Houston J. Math. 24 1998 137 171 (Pubitemid 128339456)