RTuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: esearch Article An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 628916 11 pages doi 2009 628916 Research Article An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces Mouffak Benchohra 1 Alberto Cabada 2 and Djamila Seba3 1 Laboratoire de Mathematiques Universite de Sidi Bel-Abbes BP 89 22000 Sidi Bel-Abbes Algeria 2 Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain 3 Departement de Mathématiques Universite de Boumerdes Avenue de l lndependance 35000 Boumerdes Algeria Correspondence should be addressed to Mouffak Benchohra benchohra@ Received 30 January 2009 Revised 23 March 2009 Accepted 15 May 2009 Recommended by Juan J. Nieto The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness. Copyright 2009 Mouffak Benchohra 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 The theory of fractional differential equations has been emerging as an important area of investigation in recent years. Let us mention that this theory has many applications in describing numerous events and problems of the real world. For example fractional differential equations are often applicable in engineering physics chemistry and biology. See Hilfer 1 Glockle and Nonnenmacher 2 Metzler et al. 3 Podlubny 4 Gaul et al. 5 among others. Fractional differential equations are also often an object of mathematical investigations see the papers of Agarwal et al. 6 Ahmad and Nieto 7 Ahmad and Otero-Espinar 8 Belarbi et al. 9 Belmekki et al 10 Benchohra et al. 11-13 Chang and Nieto 14 .