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

Abstract

‎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.