Existence results for a coupled system of fractional differential equations with multiple orders of fractional derivatives and integrals

Abstract

© 2018 by Eudoxus Press, LLC. All rights reserved. In this paper, we introduce a new class of coupled systems of boundary value problems for fractional differential equations which contains multiple orders of fractional derivatives and integrals, and discuss the existence and uniqueness of solutions. We apply Leray-Schauder’s alternative and Banach’s contraction mapping principle to obtain the desired results. Illustrative examples is also included.