Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Periodic Solution for a Nonlinear Fractional Differential Equ | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 324561 18 pages doi 2009 324561 Research Article Existence of Periodic Solution for a Nonlinear Fractional Differential Equation Mohammed Belmekki 1 Juan J. Nieto 2 and Rosana Rodriguez-Lopez2 1 Departement de Mathématiques Universite de Saỉda BP 138 20000 Saỉda Algeria 2 Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain Correspondence should be addressed to Rosana Rodriguez-Lopez Received 2 February 2009 Revised 10 April 2009 Accepted 4 June 2009 Recommended by Donal O Regan 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. 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. 1. Introduction Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary noninteger order. The subject is as old as the differential calculus and goes back to time when Leibnitz and Newton invented differential calculus. The idea of fractional calculus has been a subject of interest not only among mathematicians but also among physicists and engineers. See for instance 1-6 . Fractional-order models are more accurate than integer-order models that is there are more degrees of freedom in the fractional-order models. Furthermore fractional derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes due to the .