On Caputo-Hadamard fractional differential equations with nonlocal Hadamard fractional integral conditions

Abstract

This paper is concerned with the existence and uniqueness of solutions for the boundary value problem of the Caputo-Hadamard fractional differential equation supplemented with nonlocal Hadamard fractional integral boundary conditions. The existence results are obtained employing fixed point theorems due to Leray-Schauder nonlinear alternative and Krasnoselskiis, whereas the uniqueness of solution is established via the Contraction mapping principle. The obtained results are well illustrated by examples.