Research on generalized space-time fractional convection-diffusion equation

Huancheng Zhang, Jingguo Qu, Y

Abstract

By studying the basic theory of fractional differential equation, the paper extends the space-time fractional convection-diffusion equation. We use  (0 1) order fractional derivative instead of the space first derivative in the space-time fractional convection-diffusion equation and then obtain generalized space-time fractional convection-diffusion equation. We discuss its numerical solution and construct implicit difference scheme and then prove the stability and convergence of the difference scheme. Next we use the variation iteration method to discuss its approximate analytical solution and we give numerical examples to verify the effectiveness of method.