Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 364560, 17 pages
Research Article

Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia

Received 14 May 2010; Accepted 11 August 2010

Academic Editor: Juan J. Nieto

Copyright © 2010 Bashir Ahmad and Ahmed Alsaedi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.