A Fractional-in-Time Prey–Predator Model with Hunting Cooperation: Qualitative Analysis, Stability and Numerical Approximations

A prey–predator system with logistic growth of prey and hunting cooperation predators is studied. The introduction fractional time derivatives the related persistent memory strongly characterize model behavior, as many dynamical systems in applied sciences are well described by such fractional-order models. Mathematical analysis numerical simulations performed to highlight characteristics proposed model. existence, uniqueness boundedness solutions proved; stability coexistence equilibrium occurrence Hopf bifurcation investigated. Some approximations solution finally considered; obtained trajectories confirm theoretical findings. It observed that derivative has a stabilizing effect can be useful control between species.