Spatial patterns of a fractional type cross-diffusion Holling-Tanner model

In this paper, a fractional type cross-diffusion Holling-Tanner model under homogeneous Neumann boundary condition is considered. Using the maximum principle and the Harnack inequality, we obtain a priori estimates of the positive stationary solution. Nonexistence and existence of nonconstant positive stationary solution are obtained, which reveal that fractional type cross-diffusion can create spatial patterns but the random diffusion fails.