Mittag–Leffler kernel operator on prey-predator model interfusing intra-specific competition and prey fear factor

Abstract

In the present research, a prey-predator system that classifies predator species into premature and veteran species was proposed. Mathematical models of the system of species that include the impact of panic and a variety of functional reactions to the species have been recently reviewed. The consequence of fear is a reduction factor in the fundamental reproduction of the prey species. Relying on the prior research, we propose a mathematical predator-prey model employing the concept of fractional order system that contains two crucial components: intra-specific competition under mature predator density and fear, which affects the progeny of the prey community. Incorporating self-similarity characteristics is the significance of adopting a fractional order system. Following that, using memory kernel, we have interpret this model into the perspective of Caputo, that is, Atangana_Baleanu_Caputo (A_B_C) kind of fractional order derivatives. Singularity and non-locality are two of the main properties of fractional operators that make it simpler to figure out the natural behaviour of complicated systems. Details regarding the unique solution to the established model's derivation are provided. The dichotomy operator investigates the stability of the system under Hyper-Ulam`s stability method. The numerical interpolation to the suggested model generates the best precise approximate result. Through computer simulations, a thorough investigation on the predator species exhibiting intra-specific factor and prey species exhibiting fear factor is investigated. Using Adam's semi-analytical technique, we were able to derive the numerical estimates and determine the solution. The purpose to employ the Adams-Moulton approach is that it will provide more implicitly accurate results. Extensive numerical experiments are carried out using MATLAB software in order to portray the dynamical behaviour of the system. These observations lead us to the conclusion that total population expansion in the environment would be managed by the successful adoption of the fear factor in prey and the intra-species rivalry in predators.