Numerical solution of predator-prey model with Beddington-DeAngelis functional response and fractional derivatives with Mittag-Leffler kernel

Abstract

One of the major applications of the nonlinear system of differential equations in biomathematics is to describe the predator-prey problem. In this framework, the fractional predator-prey model with Beddington-DeAngelis is examined. This model is formed of three nonlinear ordinary differential equations to describe the interplay among populations of three species including prey, immature predator, and mature predator. The fractional operator used in this model is the Atangana-Baleanu fractional derivative in Caputo sense. We show first that the fractional predator-prey model has a unique solution, then propose an efficient numerical scheme based on the product integration rule. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results. The numerical method used in this paper can be utilized to solve other similar models.