A Fractional Lie Group Method For Anomalous Diffusion Equations

TL;DR

This paper introduces a fractional Lie group method tailored for solving fractional partial differential equations, demonstrated through a space-time fractional diffusion equation, enhancing analytical tools for anomalous diffusion modeling.

Contribution

It develops a fractional Lie group approach for fractional PDEs, extending classical symmetry methods to fractional differential equations.

Findings

Successfully applied to a space-time fractional diffusion equation

Demonstrates effectiveness of the fractional Lie group method

Provides a new analytical tool for anomalous diffusion equations

Abstract

Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion equation is used as an example to illustrate the effectiveness of the Lie group method.