A. Babakhani - Department of Mathematics, Faculty of Basic Science University of Technology, ۴۷۱۴۸-۷۱۱۶۷, Iran

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎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.

Boundary value problem, Nonnegative solutions, Caputo fractional derivative, Equicontinuous sets