Computational dynamics of predator-prey model with the power-law kernel

Abstract Evolution system which contains fractional derivatives can give rise to useful mathematical model for describing some important real-life or physical scenarios. Here, we suggest some numerical techniques for solving fractional-in-time reaction-diffusion models in the sense of Caputo operator. The suggested schemes are formulated with difference scheme and Fourier-spectral algorithm. In the simulation framework, it was observed that the spectral method retains the advantage of spectral accuracy over its finite difference counterpart. Both techniques are easy to adapt and extend to high-dimensions in space and time. The existence of solution, uniqueness of solution, linear stability analysis as well as the calculation of the Lyapunov exponent of the main system, are well established. Suitability of the suggested numerical techniques are tested on non-diffusive model, one-dimensional diffusive example and two-dimensional diffusive experiments.