Find out how to access previewonly content
A note on the existence of solutions for some boundary value problems of fractional differential inclusions
 Aurelian Cernea
 … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Abstract
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.
 S. Abbas, M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Commun. Math. Anal. 7 (2009), 62–72.
 A. Aghajani, Y. Jalilian, J.J. Trujillo, On the existence of solutions of fractional integrodifferential equations, Fract. Calc. Appl. Anal. 15, No 1 (2012), 44–69. DOI: 10.2478/s1354001200054; at http://www.springerlink.com/content/13110454/15/1/
 B. Ahmad, Existence of solutions for fractional differential equations of order q ∈ (2, 3] with antiperiodic boundary conditions. J. Appl. Math. Comput. 34, No 1–2 (2010), 385–391; DOI: 10.1007/s1219000903284. CrossRef
 B. Ahmad, J.J. Nieto, J. Pimentel, Some boundary value problems of fractional differential equations and inclusions. Computers and Mathematics with Applications 62, No 3 (2011), 1238–1250; doi:10.1016/j.camwa.2011.02.035. CrossRef
 B. Ahmad, V. OteroEspinar, Existence of solutions for functional differential inclusions with antiperiodic boundary conditions. Boundary Value Problems 2009 (2009), ID 625347, 1–11.
 E. Ait Dads, M. Benchohra, S. Hamani, Impulsive fractional differential inclusions involving Caputo fractional derivative. Fract. Calc. Appl. Anal. 12, No 1 (2009), 15–38; http://www.math.bas.bg/~fcaa/volume12/fcaa121/Dads_Benchohra_Hamani_FCAA121.pdf
 J.P. Aubin, A. Cellina, Differential Inclusions. Springer, Berlin (1984). CrossRef
 M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338 (2008), 1340–1350. CrossRef
 C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977).
 A. Cernea, An existence result for nonlinear integrodifferential inclusions. Comm. Applied Nonlin. Anal. 14 (2007), 17–24.
 A. Cernea, On the existence of solutions for a higher order differential inclusion without convexity. Electron. J. Qual. Theory Differ. Equ. 8 (2007), 1–8.
 A. Cernea, An existence result for a Fredholmtype integral inclusion. Fixed Point Theory 9 (2008), 441–447.
 A. Cernea, On the existence of solutions for fractional differential inclusions with boundary conditions. Fract. Calc. Appl. Anal. 12,No 4 (2009), 433–442; at http://www.math.bas.bg/~fcaa/volume12/fcaa124/Cernea fcaa 12 4.pdf
 A. Cernea, Continuous version of Filippov’s theorem for fractional differential inclusions. Nonlinear Anal. 72 (2010), 204–208. CrossRef
 Y.K. Chang, J.J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions. Mathematical and Computer Modelling 49 (2009), 605–609. CrossRef
 H. Covitz, S.B. Nadler jr., Multivalued contraction mapping in generalized metric spaces. Israel J. Math. 8 (1970), 5–11. CrossRef
 A.M.A. ElSayed, A.G. Ibrahim, Multivalued fractional differential equations of arbitrary orders. Appl. Math. Comput. 68 (1995), 15–25. CrossRef
 A.F. Filippov, Classical solutions of differential equations with multivalued right hand side. SIAM J. Control 5 (1967), 609–621. CrossRef
 Z. Kannai, P. Tallos, Stability of solution sets of differential inclusions. Acta Sci. Math. (Szeged) 61 (1995), 197–207.
 A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
 M. Kostic, Abstract timefractional equations: existence and growth of solutions, Fract. Calc. Appl. Anal. 14, No 2 (2011), 301–316; DOI: 10.2478/s1354001100184; at http://www.springerlink.com/content/13110454/14/2/
 T.C. Lim, On fixed point stability for setvalued contractive mappings with applications to generalized differential equations. J. Math. Anal. Appl. 110 (1985), 436–441. CrossRef
 I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).
 P. Tallos, A FilippovGronwall type inequality in infinite dimensional space. Pure Math. Appl. 5 (1994), 355–362.
 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