VARIATIONAL PRINCIPLE AND APPROXIMATE SOLUTION FOR THE GENERALIZED BURGERS–HUXLEY EQUATION WITH FRACTAL DERIVATIVE

Abstract

Under the non-smooth condition, many theories obtained by the assumption on the smooth condition become invalid, so a generalized Burgers–Huxley equation (GBHE) with fractal derivative is introduced in this work. The fractal variational formulation for the problem is established by using the semi-inverse method, which provides conservation laws in an energy form and possible solution structures of the equation. The two-scale transform method and variational iteration method (VIM) are used to solve the fractal GBHE. The obtained results show a great agreement with the existed results.