Fractional approximate solutions of 2D reaction–diffusion Brusselator model using the novel Laplace-optimized decomposition approach

The dynamical Brusselator reaction–diffusion system of time-fractional is used to describe chemical models and chemical processes with nonlinear oscillation. In this study, the Laplace optimized decomposition scheme is proposed for approximating solutions of three applications of the two-dimensional (2D) reaction–diffusion Brusselator model with the noninteger derivative proposed in the Caputo approach. Complete descriptions of the scheme and solution steps are utilized and mentioned. By applying the procedures of the Laplace inversion operator and truncating the optimized series, the approximate solutions are drawn, tabulated and sketched. Numerical results show the efficiency, reliability and accuracy of the technique for the nonlinear systems of partial differential equations of noninteger-different order derivatives. Finally, focused notes and futures planning works are mentioned with the most-used references.