A NOVEL APPROACH FOR FRACTAL BURGERS–BBM EQUATION AND ITS VARIATIONAL PRINCIPLE

Abstract

In this paper, the Burgers–Benjamin–Bona–Mahony (Burgers–BBM) equation is described according to the use of the fractal derivative. The variational principle of the fractal Burgers–BBM equation is successfully established by adopting the fractal semi-inverse method, which is very helpful to research the structures of fractal solution for the solitary waves and construct the conservation law. Based on the proposed variational theory, a novel approximate method is successfully proposed for the fractal Burgers–BBM equation, which is called Fractal Variational Iteration Transform Method (FVITM). The example illustrates the FVITM is an excellent and fascinating tool for fractal models.