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Fractional Calculus and Applied Analysis

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

Dingjiang Wang / Zhinan Xia
Published Online: 2015-08-04 | DOI: https://doi.org/10.1515/fca-2015-0056

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.

Keywords : ; ν)-pseudo almost automorphy; fractional differential equation; Caputo derivatives; fractional powers of operators; Leray-Schauder alternative theorem

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About the article

Received: 2014-10-11

Published Online: 2015-08-04

Published in Print: 2015-08-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 4, Pages 951–971, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2015-0056.

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