A finite difference method for a class of nonlinear fractional advection–diffusion​ equations

Abstract

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 α. The consistency and unconditionally stability of the method are shown. Finally, an example of application of this method is presented.

Keywords

• Nonlinear advection–diffusion fractional differential equations
• Finite difference method
• Riemann–Liouville fractional derivative
• Fractional Riesz derivative
• Consistency and unconditionally stability