The Analytic Methods for Solving the System of Fractional Order Brusselator Equations

Systems of fractional order Brusselator equations (SFBEs) have gained recent attention from researchers due to their relevance in the modeling of reaction-diffusion processes in triple collision, enzymatic reactions, and plasma. Finding the solution to the SFBEs has become paramount in the scientific community. Using the numerical methods for solving SFBEs yields an approximated solution, which is accompanied by errors and also requires a lot of iterations before an approximated solution is obtained. However, analytic methods that provide an exact solution to SFBEs and serve as a benchmark to validate the accuracy of an approximated solution to SFBEs have been overlooked by researchers across the world. In this paper, two effective analytic methods, known as the Adomian decomposition method (ADM) and the variational iteration method (VIM), are applied independently to obtain an exact solution to SFBEs. The two methods overcome the shortcomings of analytic methods, such as the perturbation methods and the residual power series method, which involves complex calculations and the difficulty in calculating the fractional derivative of the residual function. The ADM decomposes the nonlinear terms of the SFBEs into Adomian polynomials, which become very easy to compute. The ADM generates a series which rapidly converges to the exact solution. The VIM constructs a correction functional that yields a series that converges to the exact solution of the SFBEs. When these two methods are applied independently to obtain an exact solution to the SFBEs, both yield series that converge to the exact solution. In addition, it is observed that the ADM requires fewer terms compared to that of the VIM to obtain the exact solution to the SFBEs. The comparison analysis between the ADM and the VIM is provided.