Fractional Cauchy problems with almost sectorial operators

Applied Mathematics and Computation

Volumn 257, Issue , 2015, Pages 145-157

  Zhang, Lu ^a   Zhou, Yong ^a  

^a XIANGTAN UNIVERSITY   (China)

Author keywords

Almost sectorial operator; Caputo derivative; Cauchy problem; Fractional evolution equations; Measure of noncompactness; Riemann Liouville derivative

Indexed keywords

DIFFERENTIAL EQUATIONS;

CAPUTO DERIVATIVES; CAUCHY PROBLEMS; FRACTIONAL EVOLUTION EQUATIONS; MEASURE OF NONCOMPACTNESS; RIEMANN-LIOUVILLE DERIVATIVES; SECTORIAL OPERATOR;

LIOUVILLE EQUATION;

EID: 84924851129     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.07.024     Document Type: Article

References (40)

1. 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
2. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley New York
3. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
4. V. Lakshmikantham, S. Leela, and J.V. Devi Theory of Fractional Dynamic Systems 2009 Cambridge Academic Publishers Cambridge
5. V.E. Tarasov Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media 2010 Springer
6. Y. Zhou Basic Theory of Fractional Differential Equations 2014 World Scientific Singapore
7. R.P. Agarwal, M. Belmekki, and M. Benchohra A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative Adv. Differ. Equ. 47 2009 (Article ID 981728)
8. M. Belmekki, and M. Benchohra Existence results for fractional order semilinear functional differential equations with nondense domain Nonlinear Anal. 72 2010 925 932
9. M.A. Darwish, J. Henderson, and S.K. Ntouyas Fractional order semilinear mixed type functional differential equations and inclusions Nonlinear Stud. 16 2009 197 219
10. L. Hu, Y. Ren, and R. Sakthivel Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays Semigroup Forum 79 2009 507 514
11. O.K. Jaradat, A. Al-Omari, and S. Momani Existence of the mild solution for fractional semilinear initial value problems Nonlinear Anal. 69 2008 3153 3159
12. G.M. Mophou Existence and uniqueness of mild solutions to impulsive fractional differential equations Nonlinear Anal. 72 2010 1604 1615
13. D.N. Pandey, A. Ujlayan, and D. Bahuguna On a solution to fractional order integrodifferential equations with analytic semigroups Nonlinear Anal.: TMA 71 2009 3690 3698
14. M.H.M. Rashid, and Y. El-Qaderi Semilinear fractional integro-differential equations with compact semigroup Nonlinear Anal. 71 2009 6276 6282
15. E. Hernández, D. O'Regan, and K. Balachandran On recent developments in the theory of abstract differential equations with fractional derivatives Nonlinear Anal. 73 2010 3462 3471
16. Y. Zhou, and F. Jiao Nonlocal Cauchy problem for fractional evolution equations Nonlinear Anal.: RWA 11 2010 4465 4475
17. J. Wang, and Y. Zhou A class of fractional evolution equations and optimal controls Nonlinear Anal.: RWA 12 2011 262 272
18. J.R. Wang, M. Fečkan, and Y. Zhou On the new concept of solutions and existence results for impulsive fractional evolution equations Dyn. Partial Differ. Equ. 8 2011 345 361
19. S. Kumar, and N. Sukavanam Approximate controllability of fractional order semilinear systems with bounded delay J. Differ. Equ. 252 2012 6163 6174
20. R. Wang, D. Chen, and T.J. Xiao Abstract fractional Cauchy problems with almost sectorial operators J. Differ. Equ. 252 2012 202 235
21. H. Fan, and J. Mu Initial value problem for fractional evolution equations Adv. Differ. Equ. 49 2012
22. F. Xiao Nonlocal Cauchy problem for nonautonomous fractional evolution equations Adv. Differ. Equ. 2011 2011 1 17
23. X.B. Shu, Y.Z. Lai, and Y.M. Chen The existence of mild solutions for impulsive fractional partial differential equations Nonlinear Anal.: TMA 74 2011 2003 2011
24. K. Li, J. Peng, and J. Jia Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives J. Funct. Anal. 263 2012 476 510
25. M.M. Fall, and T. Weth Nonexistence results for a class of fractional elliptic boundary value problems J. Funct. Anal. 263 2012 2205 2227
26. A.Z.-A.M. Tazali Local existence theorems for ordinary differential equations of fractional order Ordinary and Partial Differential Equations Lecture Notes in Mathematics 964 1982 Springer Dundee pp. 652-665
27. J. Banas, and K. Goebel Measure of Noncompactness in Banach Spaces 1980 Marcel Dekker Inc. New York
28. K. Deimling Nonlinear Functional Analysis 1985 Springer-Verlag
29. H.-P. Heinz On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions Nonlinear Anal.: TMA 7 1983 1351 1371
30. V. Lakshmikantham, and S. Leela Nonlinear Differential Equations in Abstract Spaces 1969 Pergamon Press New York
31. D.J. Guo, V. Lakshmikantham, and X.Z. Liu Nonlinear Integral Equations in Abstract Spaces 1996 Kluwer Academic Dordrecht
32. H. Mönch Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces Nonlinear Anal.: TMA 4 1980 985 999
33. D. Bothe Multivalued perturbation of m-accretive differential inclusions Israel. J. Math. 108 1998 109 138
34. J.R. Wang, Y. Zhou, and M. Fečkan Abstract Cauchy problem for fractional differential equations Nonlinear Dyn. 71 2013 685 700
35. H. Markus The Functional Calculus for Sectorial Operators Operator Theory: Advances and Applications vol. 69 2006 Birkhauser-Verlag Basel
36. 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
37. A.N. Carvalho, T. Dlotko, and M.J.D. Nascimento Nonautonomous semilinear evolution equations with almost sectorial operators J. Evol. Equ. 8 2008 631 659
38. A. Pazy Semigroups of linear operators and applications to partial differential equations Applied Mathematical Sciences vol. 44 1983 Springer-Verlag Berlin, New York
39. F. Mainardi, P. Paraddisi, and R. Gorenflo Probability distributions generated by fractional diffusion equations J. Kertesz, I. Kondor, Econophysics: An Emerging Science 2000 Kluwer Dordrecht
40. L. Liu, F. Guo, and C. Wu Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces J. Math. Anal. Appl. 309 2005 638 649