A numerical method for a class of nonlinear fractional advection-diffusion equations

In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville derivative or the fractional Riesz derivative of order $\alpha$. The consistency and unconditionally stability of the method are shown. Finally, an example of application of this method is presented.