Advances in Difference Equations
Volume 2010 (2010), Article ID 508374, 9 pages
doi:10.1155/2010/508374
Almost automorphic solutions to abstract fractional differential equations
Hui-Sheng Ding1
, Jin Liang2
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
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.