Application of DGJ method for solving non-linear local fractional heat equations

describes the evolution in time of the density u of some quantity such as heat, chemical concentration, etc., where k is the thermal diffusivity coefficient [1]. But for fractal media, eq. (1) has to be modified. The local fractional calculus have been as an alternative approach proposed to study the fractal heat conduction problem [2-7]. The linear heat equation involving the local fractional derivative operators have been intensively studied over the last decade. Recent, several authors have investigated the non-linear local fractional heat equation, which can be used to model the anomalous diffusion on a fractal media [8-13]. Motivated by these results, our interest here is to solve the following non-linear local fractional heat equation: