A New Stable Algorithm for Fractional Navier–Stokes Equation in Polar Coordinate

This paper presents a new approximate method based on operational matrices of fractional integrations and differentiations for fractional Navier–Stokes equation in polar coordinate system using Legendre scaling functions as a basis. Convergence analysis as well as error analysis of the proposed methods is given. Numerical stability of the method is shown. Numerical examples are given to show the effectiveness of the proposed method. Results are compared with existing analytical methods to show the accuracy of the proposed method.