A new method of solving the Riesz fractional advection–dispersion equation with nonsmooth solution

Abstract

The Riesz fractional advection–dispersion equation with weak singularities at boundaries is solved. Our important contributions are to propose a new approach, construct successfully the fractional polynomial approximate functions with weak singularities at both endpoints in spatial direction, provide the minimum residual solution (MRS) and convergence order. Numerical examples show that the proposed method has significant advantages for dealing with weak singularities at boundaries.