A class of time-fractional-order continuous population models for interacting species with stability analysis

Abstract

In recent years, prey---predator models appearing in various fields of mathematical biology have been proposed and studied extensively due to their universal existence and importance. The paper presents the solutions of time-fractional Lotka---Volterra models with the help of analytical method of nonlinear problem called homotopy perturbation method (HPM). By using initial values, the explicit solutions of time-fractional prey and predator populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The dynamic behavior of the system investigated from the point of view of local stability. We also carry out a detailed analysis on stability of equilibrium.