Numerical approximate solutions for variable-order Riesz fractional equations via adaptive method

Abstract

This paper presents the numerical approximate solutions for variable-order Riesz fractional diffusion equation (RFDE) and Riesz fractional advection-dispersion equation (RFADE) with source term on a finite domain via adaptive method. To deal the numerical approximate solution of Riesz spatial fractional calculus, two numerical methods are provided. Numerical results are included to illustrate the results obtained.