Wavefront Dynamics in a Population Model with Anomalous Diffusion

In this paper, we consider a two-species predator–prey model with anomalous super diffusion. Such a model is in terms of fractional diffusion equations and incorporate Holling-type II and modified Leslie–Gower functional responses. We mainly study the traveling wavefront problem. For this, a theoretical analysis for the model is carried. Further, numerical simulations are performed in order to show how the evolution of wavefronts is related to meaningful parameters and verify the theoretical results. These results concerning wavefronts may provide predictions on the species spreading and invasion.