Stability analysis of fractional-order predator-prey model with anti-predator behaviour and prey refuge

This article investigates a fractional-order predator-prey model incorporating prey refuge and anti-predator behaviour on predator species. For our proposed model, we prove the existence, uniqueness, non-negativity and boundedness of solutions. Further, all biologically possible equilibrium points and their stability analysis for the proposed system are carried out with the linearization process. Moreover, by using an appropriate Lyapunov function, the global stability of the co-existence equilibrium point is studied. Finally, we provide numerical simulations to demonstrate how the theoretical approach  is  consistent.