Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations

TL;DR

This paper introduces a novel fractional variational iteration method that explicitly incorporates fractional derivatives, overcoming limitations of previous approaches that treated fractional derivatives as restricted variations.

Contribution

The paper develops a fractional variational iteration method with explicit Lagrange multipliers based on fractional variational theory, improving the handling of fractional derivatives.

Findings

The method explicitly incorporates fractional derivatives.

Lagrange multipliers are identified explicitly.

The approach enhances the solution of fractional nonlinear differential equations.

Abstract

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to overcome such shortcomings, a fractional variational iteration method is proposed. The Lagrange multipliers can be identified explicitly based on fractional variational theory.