Advances in Difference Equations
Volume 2010 (2010), Article ID 508374, 9 pages
doi:10.1155/2010/508374
Research Article

Almost Automorphic Solutions to Abstract Fractional Differential Equations

Hui-Sheng Ding,1 Jin Liang,2 and Ti-Jun Xiao3

1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
3School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 24 October 2009; Accepted 12 January 2010

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2010 Hui-Sheng Ding 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

A new and general existence and uniqueness theorem of almost automorphic solutions is obtained for the semilinear fractional differential equation Dtαu(t)=Au(t)+Dtα−1f(t,u(t))  (1<α<2), in complex Banach spaces, with Stepanov-like almost automorphic coefficients. Moreover, an application to a fractional relaxation-oscillation equation is given.