Insights into the time Fractional Belousov-Zhabotinsky System Arises in Thermodynamics

Abstract

This article employs the Shehu Adomian decomposition method to derive approximate solutions for the time-fractional Belousov-Zhabotinsky system, a phenomenon prevalent in the field of thermodynamics. This model offers a deep understanding of the core principles of nonlinear dynamics in intricate systems. This model is additionally employed to investigate bifurcations, chaotic dynamics, and other nonlinear phenomena in chemical processes. The advantage of the suggested method is that, unlike the usual Adomian process, it doesn’t involve figuring out the fractional derivative or integrals in the recursive mechanism. This makes it simple to evaluate series terms. We present Caputo, Caputo-Fabrizio, and Atangana-Baleanu in the Caputo sense fractional derivatives with the proposed method to enhance the comprehension of this intricate mechanism. We have presented various 2D and 3D graphical visualizations of the obtained solutions to demonstrate the model behaviour and the effects of the derived results by varying the fractional order. The obtained results are highly consistent with the q-homotopy analysis transform method, the fractional reduced differential transform method, and the double Laplace transform method. We also present the convergence and uniqueness of the proposed system. The results obtained with the proposed method indicate that it is simple to implement and computationally very attractive.