DYNAMICS INVESTIGATION AND NUMERICAL SIMULATION OF FRACTIONAL-ORDER PREDATOR-PREY MODEL WITH HOLLING TYPE II FUNCTIONAL RESPONSE

In the study of population dynamics, understanding the interactions between different species is crucial. Traditional models often rely on integer-order derivatives, which lack memory effects and non-local interactions. This research extends eco-epidemiological models by incorporating the CaputoFabrizio fractional derivative, providing a more accurate representation of biological processes with memory. The existence and uniqueness of positive solutions, as well as the local stability of equilibrium points in the Caputo-Fabrizio sense, are proven, ensuring the model's reliability for studying eco-epidemiological dynamics. Furthermore, the study establishes the generalized Hyers-Ulam stability for the model, ensuring robustness to small perturbations. Additionally, we introduce and analyze a novel numerical approach by constructing multistep methods of Adams-Bashforth type with step sizes ranging from 1 to 6 to solve the proposed fractional-order differential equations, enhancing the accuracy and stability of the solutions. We applied these methods to analyze three examples of fractional differential equations with known exact solutions, focusing on the dynamics for different values of the fractional order. Numerical simulations are provided to illustrate the dynamics of susceptible, infected, and predator populations, validating the theoretical findings. This comprehensive approach offers significant insights and improvements in the modeling of complex biological and epidemiological processes.