Existence results for the Hadamard fractional diσerential equations and inclusions

Abstract

In this paper, concerning non-local multi-point and integral boundary conditions, we investigate the existence and uniqueness of solutions for Hadamard fractional diσerential equations (HFDEs) and inclusions. In the case of equations, we use the Krasnoselskii fixed point theorem for the sum of two operators and Banach fixed point theorem, and Leray-Schauder’s alternative for multivalued maps and the fixed point theorem attributed to Covitz and Nadler for multivalued contractions for inclusions. Examples are given to clarify our main results. Finally, we discuss some variants of the given problem.