Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers-Fisher Equation

TL;DR

This paper applies Lie symmetry analysis to a time fractional generalized Burgers-Fisher equation, transforming it into fractional ODEs and deriving exact solutions using power series methods, advancing analytical techniques for fractional PDEs.

Contribution

It introduces a symmetry-based approach to solve the time fractional GBF equation and derives explicit solutions, which is a novel application in fractional differential equations.

Findings

Transformation of fractional PDE to fractional ODEs using symmetries

Derivation of exact solutions via power series method

Extension of symmetry analysis to fractional differential equations

Abstract

In this article, we study the Lie point symmetries for the time fractional generalized Burgers-Fisher (GBF) equation. While getting an appropriate combination of symmetries, the time fractional partial differential equation has been transformed to nonlinear fractional ordinary differential equations (ODE) using Erdelyi-Kober differential operator. Furthermore, using power series method, we get the exact solution of the nonlinear fractional GBF equation with the arbitrary nonlinearity.