Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID i58789 10 pages doi 2010 158789 Research Article Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations Fang Li1 and Gaston M. N Guerekata2 1 School of Mathematics Yunnan Normal University Kunming 650092 China 2 Department of Mathematics Morgan State University 1700 East Cold Spring Lane Baltimore MD 21251 USA Correspondence should be addressed to Fang Li fangli860@ Received 1 April 2010 Accepted 17 June 2010 Academic Editor Tocka Diagana Copyright 2010 F. Li and G. M. N Guerekata. 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. We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations dqu t dtq Au f f t u t f0 a t - s g s u s ds t e 0 T u 0 u0 in a Banach space X where 0 q 1. New results are obtained by fixed point theorem. An application of the abstract results is also given. 1. Introduction An integrodifferential equation is an equation which involves both integrals and derivatives of an unknown function. It arises in many fields like electronic fluid dynamics biological models and chemical kinetics. A well-known example is the equations of basic electric circuit analysis. In recent years the theory of various integrodifferential equations in Banach spaces has been studied deeply due to their important values in sciences and technologies and many significant results have been established see . 1-11 and references therein . On the other hand many phenomena in Engineering Physics Economy Chemistry Aerodynamics and Electrodynamics of complex medium can be modeled by fractional differential equations. During the past decades such problem attracted many researchers see 1 12-21 and references therein . However
