Abstract and Applied Analysis
Volume 2013 (2013), Article ID 592964, 8 pages
Research Article

The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

1Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol 47148-71167, Iran
2Department of Mathematics and Computer Science, Cankaya University, Turkey
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
4Institute of Space Sciences, P.O. Box MG-23, r 76900 Magurele-Bucharest, Romania
5Department of Mathematics, Texas A & M University-Kingsville, 700 University, Boulevard Kingsville, USA
6Department of Mathematics, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Received 28 October 2012; Accepted 2 February 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Azizollah Babakhani et al. 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 prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in such that is continuous and is a phase space.