Boundary Value Problems
Volume 2009 (2009), Article ID 324561, 18 pages
doi:10.1155/2009/324561
Existence of periodic solution for a nonlinear fractional differential equation
Mohammed Belmekki1
, Juan J. Nieto2
and Rosana Rodríguez-López3
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
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.