Normalized time-fractional predator–prey model with landscape features

We propose a normalized time-fractional predatorprey model with landscape features. The mathematical model uses a normalized fractional derivative to describe memory effects in predator and prey populations. This model is more flexible than the standard integer-order model. To solve the model, we use an operator-splitting method that separates the reaction and diffusion parts. This method reduces computation time and gives stable and accurate results. Numerical tests show how the fractional order affects pattern formation. The computational results show that the fractional order changes when patterns appear, how long they last, and whether the population distribution becomes uniform or nonuniform. Our numerical results indicate the potential of combining normalized time-fractional modeling with landscape heterogeneity to study complex ecological processes, and suggest that the proposed model provides a flexible tool for investigating spatiotemporal dynamics in population systems.