Analysis of A Fractional-Order Competition Model with Common Inhibitory Effect

Abstract

In this paper, we have introduced a fractional-order competition model of two interacting species with common inhibitory effect. The two analytical methods, homotopy perturbation method (HPM) and variational iteration method (VIM), have been successfully implemented for solving our non-linear competition model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial values, the explicit solutions of two interacting species populations for different particular cases have been derived with the help of HPM and VIM. This paper represents an analytical as well as numerical comparison between the two methods for solving our fractional order competition model for different fractional order. Numerical results show that the two approaches are easy to implement, extremely efficient to solve this complicated model and are in good agreement with the exact solutions. Analytical results also show that the two techniques require less computational work than other existing analytical methods with easy to solve terms for obtaining quantitatively reliable results.