Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation

Abstract

AbstractIn this article, we studied the time‐fractional Burgers–Huxley equation using the natural transform decomposition method. The fractional operator is treated in the Caputo, Caputo–Fabrizio, and Atangana–Baleanu senses. We employed the natural transform with the Adomian decomposition process on time‐fractional Burgers–Huxley equation to obtain the solution. To establish the uniqueness and convergence of the accomplished solution, the Banach's fixed point theorem is used. The obtained findings are visually shown in two‐ and three‐dimensional graphs for various fractional orders. To illustrate the efficacy of the method under discussion, numerical simulations are provided. The proposed solution captures the behavior of the reported findings for various fractional orders. A comparative study was conducted to ascertain the proposed method's correctness. The findings of this study establish that the technique investigated is both efficient and accurate for solving nonlinear fractional differential equations that arise in science and technology.