TY - JOUR
T1 - Numerical Solutions for Fractional Burgers’ Equation Based on Laplace Transform
AU - Sun , Weiye
AU - An , Yulian
AU - Gao , Yijin
AU - Luo , Songting
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 318
EP - 333
PY - 2025
DA - 2025/02
SN - 7
DO - http://doi.org/10.12150/jnma.2025.318
UR - https://global-sci.org/intro/article_detail/jnma/23828.html
KW - Fractional Burgers’ equation, Laplace transform, Caputo derivative, numerical simulations.
AB - <p style="text-align: justify;">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.</p>