ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Fractional Differential Equations System for Commercial Fishing under Predator-Prey Interaction

Journal of Applied Nonlinear Dynamics 2(4) (2013) 409--417 | DOI:10.5890/JAND.2013.11.007

$^{1}$ Mathematics Department, Shiraz University, Shiraz, Iran

$^{2}$ Department of Economics, Tokyo Metropolitan University, Hachioji-shi, Tokyo, Japan

$^{3}$ Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran

Abstract

In this article we introduce and analyze a mathematical model of commercial fishing as a dynamical system presented by fractional differential equations (FDE). In the model two different species of fish are interacting as predator and prey. We discuss the long-run properties of this system, including stability of equilibrium points, non-existence of limit cycle and periodic solution for the movement of fish stocks for both species. In deriving our mathematical model, instead of customary use of classical positive integer order of differential equations, we use fractional order derivatives. As we will discuss, non-local properties of FDE and its advantages in modeling problems with non-smooth domains will yield more accurate results in comparison with ordinary differential equation counterpart.

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