Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method

TL;DR

This paper develops analytic solutions for nonlinear fractional Burgers-type equations using the Invariant Subspace Method, addressing equations with time and space fractional derivatives and their generalizations.

Contribution

It introduces a systematic approach to solve a class of fractional Burgers equations analytically using invariant subspaces, including generalized and variable-coefficient cases.

Findings

Derived explicit solutions for time-fractional Burgers equations

Extended solutions to equations with space and time fractional derivatives

Provided analytical methods for generalized and forced fractional Burgers equations

Abstract

In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation. Some generalizations linked to the forced time-fractional Burgers equations and variable-coefficient diffusion are also considered. Finally we study a Burgers-type equation involving both space and time-fractional derivatives.