Global dynamics of a fractional-order Leslie-Gower model with Allee effect

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free point co-existence point. By using Adams-Bashfort-Moulton for system, we perform some numerical simulations justify theoretical results.