Analytical Solution and Numerical Simulation of the Two-Dimensional Time-Fractional Reaction-Diffusion Brusselator System

Abstract

In this study, the Natural decomposition method is introduced to solve the two-dimensional nonlinear time-fractional reaction-diffusion Brusselator system. The fractional derivatives are described in the Caputo sense. The closed-form solution, as it is a vital momentary in solving sophisticated nonlinear differential equations, was obtained and to be investigated thoroughly in the present study. Additionally, the approximate semi-analytic solution is presented as a rapidly convergent series, which is proved via tables and illustrations. The nonlinearity of the equations is decomposed using the Adomian polynomials. All computations were executed via Mathematica symbolic computational package.