A New Numerıcal Scheme Applıed On Re-vısıted Nonlınear Model Of Predator-Prey Based On Derıvatıve Wıth Non-Local And Non-Sıngular Kernel

Abstract

A new concept of dynamical system of predator-prey model is presented in this paper. The model takes into account the memory of interaction between the prey and predator due to the inclusion of fractional differentiation. In addition, the model takes into account the inherent disposition of a prey or predator toward hunting or defending in time. Analysis of existence and uniqueness of the solutions is presented. A numerical method is used to generate some simulations as the fractional orders change from one to zero. A new traveling waves patterns are obtained.