Exact solution for local fractional Diffusion and Wave Equations on Cantor Sets

Abstract

In this paper, the local fractional homotopy perturbation method and the local fractional Sumudu transform are used to study diffusion and wave equations defined on Cantor sets with the fractal conditions with local fractional derivatives. The LFSHPM analytical method minimizes the computational size and may be applied directly to fractional differential equations without any linearization, discretization of variables, transformation, or restrictive assumptions. It provides series solutions that converge quickly in a few iterations. The proposed analytical method is successfully applied to diffusion and wave equations defined on cantor sets with fractal conditions, and proved to be highly efficient and computational accurate