Symmetry Classification and Exact Solutions of a Variable Coefficient Nonlinear Space-Time Fractional Burgers' Equation

TL;DR

This paper explores the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation, deriving invariant solutions and exact solutions using Lie symmetry analysis and the invariant subspace method.

Contribution

It introduces a comprehensive symmetry analysis and solution methods for a fractional Burgers' equation with variable coefficients, expanding the understanding of its solutions.

Findings

Derived fractional Lie symmetries and infinitesimal generators.

Obtained group invariant solutions of the fractional Burgers' equation.

Generated exact solutions using the invariant subspace method.

Abstract

In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the infinitesimal generators some group invariant solutions are deduced. Further, some exact solutions of fractional Burgers' equation are generated by the invariant subspace method.