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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 176180, 8 pages
http://dx.doi.org/10.1155/2013/176180
Research Article

Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with 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
3Institute of Space Sciences, P.O. Box, MG-23, 76900 Magurele-Bucharest, Romania

Received 11 June 2013; Accepted 15 August 2013

Academic Editor: Ali H. Bhrawy

Copyright © 2013 Hadi Karami 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.

Abstract

We discuss the existence and uniqueness of solution for two types of fractional order ordinary and delay differential equations. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle to prove the uniqueness of solution and then Krasnoselskii's fixed point theorem to show the existence of the solution under certain conditions in a Banach space.