Dynamic behaviors of the non-linear local fractional heat conduction equation on the cantor sets

Abstract

Based on the local fractional derivative, a fractal non-linear heat conduction equation, which can model the behavior of the heat transfer in the fractal medium, is extracted in this work. On defining the Mittag-Leffler function on the Cantor sets, two special functions namely the TH?(??) function and CH?(??) function are constructed, and then are employed along with Yang?s non-differentiable transfor?mation seek for the non-differentiable exact solutions. The obtained results confirm that the proposed method iseffective and powerful, and can provide a promising way to find the exact solutions of the fractal PDE.