Electron. J. Diff. Equ., Vol. 2010(2010), No. 20, pp. 1-16.

Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions

Samira Hamani, Mouffak Benchohra, John R. Graef

Abstract:
In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.

Submitted September 8, 2009. Published January 28, 2010.
Math Subject Classifications: 26A33, 34A60, 34B15.
Key Words: Boundary-value problem; differential inclusion; fractional integral; Caputo fractional derivative; existence; uniqueness; fixed point; integral conditions.

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Samira Hamani
Laboratoire de Mathématiques
Université de Sidi Bel Abbès
BP 89, 2000 Sidi Bel Abbès, Algérie
email: hamani_samira@yahoo.fr
Mouffak Benchohra
Laboratoire de Mathématiques
Université de Sidi Bel Abbès
BP 89, 2000 Sidi Bel Abbès, Algérie
email: benchohra@univ-sba.dz
John R. Graef
Department of Mathematics
University of Tennessee at Chattanooga
Chattanooga, TN 37403-2504, USA
email: John-Graef@utc.edu

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