Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions

Abstract

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a boundary value problem of fractional differential equations with nonlocal and average type integral boundary conditions. The Leray–Schauder nonlinear alternative, Krasnoselskii’s fixed point theorem and Banach’s fixed point theorem together with Holder inequality are applied to construct proofs for the main results. Examples illustrating the obtained results are also presented.