The Effect of Fractional-Order Derivative for Pattern Formation of Brusselator Reaction-Diffusion Model Occurring in Chemical Reactions

The space fractional PDEs (SFPDEs) have attracted a lot of attention. Developing high-order and stable numerical algorithms for them is the main aim of most researchers. This research work presents a fractional spectral collocation method to solve the fractional models with space fractional derivative which is defined based upon the Riesz derivative. First, a second-order difference formulation is used to approximate the time derivative. The stability property and convergence order of the semi-discrete scheme are analyzed. Then, the fractional spectral collocation method based on the fractional Jacobi polynomials is employed to discrete the spatial variable. In the numerical results, the effect of fractional order is studied.