On the existence of nonnegative solutions of nonlocal boundary value problems for a class of fractional differential equations

Abstract

This article studies the existence of nonnegative solutions for a boundary value problem (BVP) of nonlinear fractional differential equations. Some new existence results are obtained by applying Kranoselskii`s fixed-point theorem in a cone. First we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela-Ascoli theorem is used to take $C^1$ limits of sequences of such solutions. As an application, we give an examples that illustrate our results.