Abstract
In this paper, the local derivative in time is replaced with the Caputo-Fabrizio fractional derivative of order $ \alpha\in(0, 1) $. A two-step fractional version of the Adams-Bashforth method is formulated for the approximation of this derivative. To enhance the correct choice of parameters when numerically simulating the full-system, we examine the stability analysis of the main equation. Two important examples are drawn to explore the dynamic richness of the predator-prey model with Holling type. Simulation results at different instances of $ \alpha $ is in agreement with the theoretical findings.
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