Pseudo almost automorphic behavior of  solutions to a semi-linear fractional differential equation

Yong-Kui Chang; Xiao-Xia Luo

Vol. 20 No. 1 (2015)

Regular Articles

Pseudo almost automorphic behavior of solutions to a semi-linear fractional differential equation

Published 2015-02-26

Yong-Kui Chang
Xiao-Xia Luo

Yong-Kui Chang
Department of Mathematics, Lanzhou Jiaotong University

Xiao-Xia Luo
Department of Mathematics, Lanzhou Jiaotong University

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Abstract

In this paper, we shall deal with $\mu$-pseudo almost automorphic solutions to a semi-linear fractional differential equation by new concept of $\mu$-pseudo almost automorphic functions presented recently. We first establish some new properties of $\mu$-pseudo almost automorphic functions, and then we apply the results obtained to prove some existence theorems combined with the Leray-Schauder alternative theorem.

Keywords

fractional differential equation, $\mu$-pseudo almost automorphic function, composition theorems, Leray-Schauder alternative theorem

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