![]() ![]() ![]() Koo, Stability for Caputo fractional differential systems, Abstr. Bozkurt, Stability analysis of a fractional order differential equation system of a GBM-IS interaction depending on the density, Appl. Alam, Impact of predator incited fear and prey refuge in a fractional order prey predator model, Chaos Soliton. Martiradonna, Optimal control of invasive species through a dynamical systems approach, Nonlinear Anal.-Real, 49 (2019), 45–70. Gomez-Aguilar, Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena, Eur. Hilker, Hunting cooperation and Allee effects in predators, J. The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.Ĭitation: Ali Yousef, Ashraf Adnan Thirthar, Abdesslem Larmani Alaoui, Prabir Panja, Thabet Abdeljawad. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. At first, we show that the system has non-negative solutions. This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. ![]()
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