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18 Mar 2012
A note on the existence of solutions for some boundary value problems of fractional differential inclusions
 Aurelian Cernea
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We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with families of mixed and closed boundary conditions. We establish Filippov type existence results in the case of nonconvex setvalued maps.
 Abbas, S., Benchohra, M. (2009) Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Commun. Math. Anal. 7: pp. 6272
 Aghajani, A., Jalilian, Y., Trujillo, J.J. (2012) On the existence of solutions of fractional integrodifferential equations. Fract. Calc. Appl. Anal. 15: pp. 4469
 Ahmad, B. (2010) Existence of solutions for fractional differential equations of order q ∈ (2, 3] with antiperiodic boundary conditions. J. Appl. Math. Comput. 34: pp. 385391 CrossRef
 Ahmad, B., Nieto, J.J., Pimentel, J. (2011) Some boundary value problems of fractional differential equations and inclusions. Computers and Mathematics with Applications 62: pp. 12381250 CrossRef
 Ahmad, B., OteroEspinar, V. (2009) Existence of solutions for functional differential inclusions with antiperiodic boundary conditions. Boundary Value Problems 2009: pp. 111
 Dads, E. A., Benchohra, M., Hamani, S. (2009) Impulsive fractional differential inclusions involving Caputo fractional derivative. Fract. Calc. Appl. Anal. 12: pp. 1538
 Aubin, J.P., Cellina, A. (1984) Differential Inclusions. Springer, Berlin CrossRef
 Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A. (2008) Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338: pp. 13401350 CrossRef
 Castaing, C., Valadier, M. (1977) Convex Analysis and Measurable Multifunctions. Springer, Berlin
 Cernea, A. (2007) An existence result for nonlinear integrodifferential inclusions. Comm. Applied Nonlin. Anal. 14: pp. 1724
 Cernea, A. (2007) On the existence of solutions for a higher order differential inclusion without convexity. Electron. J. Qual. Theory Differ. Equ. 8: pp. 18
 Cernea, A. (2008) An existence result for a Fredholmtype integral inclusion. Fixed Point Theory 9: pp. 441447
 Cernea, A. (2009) On the existence of solutions for fractional differential inclusions with boundary conditions. Fract. Calc. Appl. Anal. 12: pp. 433442
 Cernea, A. (2010) Continuous version of Filippov’s theorem for fractional differential inclusions. Nonlinear Anal. 72: pp. 204208 CrossRef
 Chang, Y.K., Nieto, J.J. (2009) Some new existence results for fractional differential inclusions with boundary conditions. Mathematical and Computer Modelling 49: pp. 605609 CrossRef
 Covitz, H., Nadler, S.B. (1970) Multivalued contraction mapping in generalized metric spaces. Israel J. Math. 8: pp. 511 CrossRef
 ElSayed, A.M.A., Ibrahim, A.G. (1995) Multivalued fractional differential equations of arbitrary orders. Appl. Math. Comput. 68: pp. 1525 CrossRef
 Filippov, A.F. (1967) Classical solutions of differential equations with multivalued right hand side. SIAM J. Control 5: pp. 609621 CrossRef
 Kannai, Z., Tallos, P. (1995) Stability of solution sets of differential inclusions. Acta Sci. Math. (Szeged) 61: pp. 197207
 Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam
 Kostic, M. (2011) Abstract timefractional equations: existence and growth of solutions. Fract. Calc. Appl. Anal. 14: pp. 301316
 Lim, T.C. (1985) On fixed point stability for setvalued contractive mappings with applications to generalized differential equations. J. Math. Anal. Appl. 110: pp. 436441 CrossRef
 Podlubny, I. (1999) Fractional Differential Equations. Academic Press, San Diego
 Tallos, P. (1994) A FilippovGronwall type inequality in infinite dimensional space. Pure Math. Appl. 5: pp. 355362
 Title
 A note on the existence of solutions for some boundary value problems of fractional differential inclusions
 Journal

Fractional Calculus and Applied Analysis
Volume 15, Issue 2 , pp 183194
 Cover Date
 20120601
 DOI
 10.2478/s1354001200134
 Print ISSN
 13110454
 Online ISSN
 13142224
 Publisher
 SP Versita
 Additional Links
 Topics
 Keywords

 34A60
 34A08
 35R11
 fractional differential inclusion
 Caputo fractional derivative
 boundary value problem
 mixed and closed boundary conditions
 Authors

 Aurelian Cernea ^{(1)}
 Author Affiliations

 1. Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, 010014, Bucharest, Romania