In this work, we propose an efficient multi-stage homotopy perturbation method to find an analytic solution to the fractional Lotka-Volterra model. We obtain its order of accuracy, and we study the stability of the system. Moreover, we present several examples to show of the effectiveness of this method, and we conclude that the value of the derivative order plays an important role in the trajectories velocity.

In this paper, we study a generalization of a Lotka–Volterra system with Holling type III functional response, where the Caputo fractional derivative is considered. Applying a multistage homotopy perturbation method, we obtain an analytical solution for the system. Moreover, analyzing the eigenvalues of the Jacobian matrix around the equilibria, we find sufficient conditions in order to guarantee the local stability and we present several examples to illustrate the behavior of solutions.