He’s fractal calculus and its application to fractal Korteweg-de Vries equation

Abstract

He’s fractal calculus is a powerful and effective tool to dealing with natural phenomena in a fractal space. In this paper, we study the fractal KdV equation with He’s fractal derivative. We first adopt the two-scale transform method to convert the fractal KdV equation into its traditional partner in a continuous space. Finally, we successfully use He’s variational iteration method (HVIM) to obtain its approximate analytical solution.