Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions

In this paper, we investigate a new class of mixed initial value problems of Hadamard and Riemann- Liouville fractional integro-differential inclusions. The existence of solutions for convex valued (the upper semicontinuous) case is established by means of Krasnoselskii s fixed point theorem for multivalued maps and nonlinear alternative criterion, while the existence result for non-convex valued maps (the Lipschitz case) relies on a fixed point theorem due to Covitz and Nadler. Illustrative examples are also included.