Pseudo Almost Automorphic Solution of Semilinear Fractional Differential Equations with the Caputo Derivatives

Dingjiang Wang 1  and Zhinan Xia 1
  • 1 Department of Applied Mathematics Zhejiang University of Technology Hangzhou, Zhejiang, 310023, CHINA

Abstract

In this paper, we deal with existence and uniqueness of (μ, ν)-pseudo almost automorphic mild (classical) solution to semilinear fractional differential equations with the Caputo derivatives. The main results are obtained by means of the fixed point theory, Leray-Schauder alternative theorem and fractional powers of operators. Moreover, an application to fractional predator-prey system with diffusion is given.

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Fractional Calculus and Applied Analysis (FCAA) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order.

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