Title: Stability conditions of a coupled system of fractional q-difference Lotka-Volterra model

Authors: Kuikui Ma; Zhenlai Han; Yongxiang Zhang

Addresses: School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China ' School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P.R. China

Abstract: In this paper, we study the existence and uniqueness of solutions for the boundary value problems of a class of coupled system of fractional q-difference Lotka-Volterra equations involving the Caputo fractional derivative. The results of this paper can provide a reference for determining whether a given predator-prey system can reach equilibrium states after a certain number of years. Our results are based on the non-linear alternative of Leray-Schauder type and Banach's fixed point theorem. At applications, the stability of fractional q-difference Lotka-Volterra equations is presented to illustrate our main results.

Keywords: boundary value problems; coupled systems; fractional q-difference equations; fixed point theorems; Lotka-Volterra equations; stability conditions; Caputo fractional derivative; predator-prey systems.

DOI: 10.1504/IJDSDE.2016.081815

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.4, pp.305 - 317

Received: 26 Jan 2016
Accepted: 02 May 2016
Published online: 26 Jan 2017 *

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