Pattern formation in a fractional-order reaction-diffusion predator-prey model with Holling-III functional response

In this paper, we investigate the spatiotemporal dynamics of a fractional-order predator-prey reaction-diffusion model (frPDE) with Holling-type III functional response. We prove that this is not the integer-order reaction-diffusion model, but the frPDE model exhibits fraction-diffusion-induced instability (i.e., Turing instability), which is induced by the fractional-order and diffusion together. Furthermore, via numerical simulations, the frPDE model dynamics exhibits both fractional-order and diffusion controlled Turing pattern formation, which shows that the dynamics of the frPDE model is not simple, but rich and complex.