Fractional-Order Discrete Predator–Prey System of Leslie Type: Existence, Stability, and Numerical Simulation

This study explores a fractional-order (FO) discrete predator prey (PP) system of Leslie type (LT) by incorporating fractional differences in the Caputo-Fabrizio-Riemann (CFR) sense. We rigorously establish the existence and uniqueness of solutions and provide a comprehensive stability analysis. A novel numerical scheme is developed to approximate the system’s dynamics, yielding deeper insights into PP interactions under FO effects. Furthermore, we validate our theoretical findings using numerical simulations, which confirm the robustness and accuracy of the proposed model. The results underline the significance of fractional calculus (FC) in ecological modeling and pave the way for future investigations in population dynamics.