VARIATIONAL PRINCIPLE OF THE 2-D STEADY-STATE CONVECTION-DIFFUSION EQUATION WITH FRACTAL DERIVATIVES

The convection-diffusion equation describes a convection and diffusion process, which is the cornerstone of electrochemistry. The process always takes place in a porous medium or on an uneven boundary, and an abnormal diffusion occurs, which will lead to deviations in prediction of the convection-diffusion process. To overcome the problem, a fractal modification is suggested to deal with the "ab-normal" problem, and a 2-D steady-state convection-diffusion equation with fractal derivatives in the fractal space is established. Furthermore, its fractal variational principle is obtained by the semi-inverse method. The fractal varia-tional formula can not only provide the conservation law in the fractal space in the form of energy, but also give the possible solution structure of the equation.