In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.

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The sufficient conditions are established for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative.

In this paper, we use some background concerning multivalued functions and set-valued analysis, the fixed point theorem of Bohnenblust-Karlin and the method of upper and lower solutions to investigate the existence of solutions for a class of boundary value problem of functional differential inclusions involving the Caputo-Hadamard fractional derivative.

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In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.