A NEW NUMERICAL SCHEME APPLIED ON RE-VISITED NONLINEAR MODEL OF PREDATOR-PREY BASED ON DERIVATIVE WITH NON-LOCAL AND NON-SINGULAR KERNEL

摘要

A new concept of dynamical system of predator-prey model is pre- sented in this paper. The model takes into account the memory of interaction between the prey and predator due to the inclusion of fractional differentia- tion. 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.