A fractal-fractional-order modified Predator-Prey mathematical model with immigrations

This manuscript aims to study a modified predator-prey model's existence, stability, and dynamics under the newly developed fractal-fractional order operator in the Caputo-Fabrizio sense. The existence theory of the proposed model carries out through the Leray-Schauder alternative and sufficient conditions for stability are established using the classical technique of nonlinear functional analysis. The numerical results are obtained by the fractal-fractional Adam-Bashforth method in the Caputo-Fabrizio sense. The numerical results show that small immigrations invoke stable convergence in the predator-prey ecosystem. This means that a small number of sporadic immigrants can stabilize natural predator-prey populations. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.