Dynamic analysis of a fractional-order single-species model with diffusion

In this paper, we consider a fractional-order single-species model, which is composed of several patches connected by diffusion. We first prove the existence, uniqueness, non-negativity, and boundedness of solutions for the model, as desired in any population dynamics. Moreover, we also obtain some sufficient conditions ensuring the existence and uniform asymptotic stability of the positive equilibrium point for the investigated system. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the theoretical results.