New Lagrange multipliers for the time fractional Burgers' equation

TL;DR

This paper develops an analytical approach using Lagrange multipliers and the variational iteration method to find approximate solutions for the fractional generalized -time Burgers' equation, covering cases where the fractional order  is between 0 and 2.

Contribution

It introduces new Lagrange multipliers tailored for the fractional Burgers' equation and applies the variational iteration method to obtain approximate solutions.

Findings

Derived approximate solutions for  between 0 and 2.

Extended the variational iteration method to fractional derivatives.

Provided analytical techniques for fractional Burgers' equations.

Abstract

Using the fractional derivative, considered in the Caputo sense, we study an analytical technique associated with the variational iteration method for the fractional generalized $\alpha$-time Burgers' equation with $\alpha>0$ and obtain approximate solutions in particular cases $0<\alpha\leq 1$ and $1<\alpha\leq 2$.