Boundary Value Problems
Volume 2009 (2009), Article ID 324561, 18 pages
doi:10.1155/2009/324561
Research Article

Existence of Periodic Solution for a Nonlinear Fractional Differential Equation

Mohammed Belmekki,1 Juan J. Nieto,2 and Rosana Rodríguez-López2

1Département de Mathématiques, Université de Saïda, BP 138, 20000 Saïda, Algeria
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Received 2 February 2009; Revised 10 April 2009; Accepted 4 June 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Mohammed Belmekki 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 study the existence of solutions for a class of fractional differential equations. Due to the singularity of the possible solutions, we introduce a new and proper concept of periodic boundary value conditions. We present Green's function and give some existence results for the linear case and then we study the nonlinear problem.