Abstract
In this paper, we have investigated the fractional-order Brusselator model for the approximate analytical solution. The concerned coupled system of nonlinear fractional-order partial differential equations (PDEs) has been considered in many research articles to describe various real-world problems. Nonlinear dynamical systems are increasingly used in autocatalytic chemical reactions. These types of autocatalytic chemical reaction models have a variety of applications in several physical systems. The Brusselator model is one of the intensively used autocatalytic models. We have obtained the approximate solution of the considered fractional nonlinear Brusselator model in the Caputo sense by using the Laplace–Adomian decomposition method (LADM). We have established a general scheme for the solution to the proposed model by applying the LADM. We then testified two examples to demonstrate our analysis. The results we have obtained ensure the accuracy and effectiveness of the proposed technique. The said technique does not require any kind of prior discretization or collocation. Also, with the help of Matlab, we have presented 2D and 3D plots for the approximate solution.