Geodesic
Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 15-38.

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In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered.
Keywords: Initial Value Problem, Fractional Differential Inclusions, Impulses, Caputo Fractional Derivative, Fractional Integral, Selection, Existence, Fixed Point Theorem, 26A33, 34A37 
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Ait Dads, E.; Benchohra, M.; Hamani, S. Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 15-38. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a1/