Asymptotic Behavior of Fractional-Order Holling Type II Prey-Predator With Hunting Cooperation

In this paper, we developed a fractional-order one-prey two-predator system considering Holling type II functional response and hunting cooperation. We also investigated the interspecific dynamics of prey between the I predator and the II predator. We also proved the boundedness, positivity, the uniqueness, and the existence of the solutions of our system. In addition, we showed the local stability and the global stability behavior of the equilibria, and a Hopf bifurcation occurred. Also, we computed the numerical simulations of the solutions to demonstrate the consistency of the analytical approach, in which the theoretical observations are confirmed by the trajectories and phase portraits finally. It is observed that our system is impacted by hunting cooperation, and the fractional-order derivative stabilizes the system.