(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
The Burgers’ equation has widespread applications across various fields. In this paper, we propose an efficient approach for obtaining the numerical solution to the time-fractional Burgers’ equation. We extend the classical Burgers’ equation to its fractional form by introducing Caputo derivatives. Using the Cole-Hopf transform, we reformulate the problem into a fractional diffusion equation. The Laplace transform method is then applied to convert the equation into an ordinary differential equation (ODE), which can be solved analytically. However, due to the lack of an inverse Laplace transform for this specific form, numerical approximation methods are then utilised to approximate the true solution. Numerical simulations are provided to demonstrate the stability and accuracy of the proposed method.