Analysis of a Predator-prey Population Model

In this paper, we have introduced a fractional-ordered predator-prey population model which has been successfully solved with the help of two powerful analytical methods, namely, Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. Using initial values, we have derived the explicit solutions of predator-prey populations for different particular cases by using HPM and VIM. This paper represents an analytical as well as numerical comparison between these two methods for solving our fractional-ordered predator-prey population model for different fractional orders. Our analytical and numerical results show that these two techniques require less computational work and provide the approximate solutions with easily computable components. These methods are extremely efficient for obtaining quantitatively reliable results.