Lie group classifications and exact solutions for time-fractional Burgers equation

TL;DR

This paper introduces a fractional Lie group method to solve time-fractional partial differential equations, demonstrating its effectiveness through the derivation of exact solutions for a fractional Burgers equation.

Contribution

It extends the Lie group method to fractional PDEs and provides a new approach for finding exact solutions of such equations.

Findings

Exact solutions for the time-fractional Burgers equation were obtained.

The fractional Lie group method is effective for solving fractional PDEs.

Abstract

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.