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.