Existence of solutions for nonlocal boundary value problem for Caputo nonlinear fractional differential inclusion

This paper deals with the existence of solutions for nonlinear fractional differential inclusions supplemented with three-point boundary conditions. First, we investigate it for $ L^{1}$-Caratheodory convex-compact valued multifunction. Then, we investigate it for nonconvex-compact valued multifunction via some conditions. Two illustrative examples are presented at the end of the paper to illustrate the validity of our results.

Keywords:

Existence, Fractional differential inclusion Fixed point theorem, Nonlocal boundary,

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