Existence and uniqueness of solutions for the nonlinear retarded and advanced implicit Hadamard fractional differential equations with nonlocal conditions

Abstract

In this paper, we use the Banach contraction mapping principle and the Krasnoselskii fixed point theorem to obtain the existence and uniqueness of solutions for nonlinear retarded and advanced implicit Hadamard fractional differential equations with nonlocal conditions. The results obtained here extend the work of Benchohra, Bouriah and Henderson <cite>ben</cite>. Two examples are also given to illustrate the results.