Modelling and Analysis of Predation System with Nonlocal and Nonsingular Operator

Abstract

A novel system of predation involving two individuals or species which interact in a nonlinear fashion is modelled with the Atangana-Baleanu fractional derivative of order (Formula presented) in the sense of Caputo. This derivative has been used to model some important real-life phenomena such as heat flow, fractals, diffusion and groundwater flows, among many others. The local and global stability analysis of such model is given to enable us to accurately provide a good choice of parameters when numerically simulating the full process. Some numerical results for different instances of fractional power are given in one and two dimensions.