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
