A new non-standard finite difference method for analyzing the fractional Navier-Stokes equations

In this paper the numerical solution of the fractional Navier-Stokes equations (FNSE) is derived by means of a new non-standard finite difference method (NSFDM). The fractional differential operators are taken in sense of the Riesz fractional derivative. The pressure driven by the flow between two parallel plates is solved with the NSFDM and a modified trapezoidal quadrature rule of fractional order. The stability and convergence of the proposed scheme are proved. Numerical examples illustrate the effectiveness of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.