Mathematical Modelling of a Delay Prey-Predator System using Caputo Fractional Derivatives

In this paper introduces a nonlinear fractional-order prey–predator model to describe the interaction between one prey species and two predator species in an ecological system. These model are formulated with the use of Caputo fractional derivative with time delay to represent memory and hereditary effects that naturally arise in biological processes. The model includes prey growth dynamics and nonlinear interaction terms among the three species. Local stability of the system is examined at different equilibrium points using the Jacobian matrix method. Numerical solutions of the fractional delay system are obtained using the fractional Adams–Bash forth –Moulton predictor–corrector scheme. The influence of different fractional orders 0 < α