Numerical Solutions for Fractional Burgers’ Equation Based on Laplace Transform (Journal of Nonlinear Modeling and Analysis, 2025)
The Burgers’ equation has widespread applications across variousfields. In this paper, we propose an efficient approach for obtaining the numerical solution to the time-fractional Burgers’ equation. We extend the classicalBurgers’ equation to its fractional form by introducing Caputo derivatives.Using the Cole-Hopf transform, we reformulate the problem into a fractionaldiffusion equation. The Laplace transform method is then applied to convertthe equation into an ordinary differential equation (ODE), which can be solvedanalytically. However, due to the lack of an inverse Laplace transform for thisspecific form, numerical approximation methods are then utilised to approximate the true solution. Numerical simulations are provided to demonstratethe stability and accuracy of the proposed method.