Application of Triple- and Quadruple-Generalized Laplace Transform to (2+1)- and (3+1)-Dimensional Time-Fractional Navier–Stokes Equation

Abstract

In this study, the solution of the (2+1)- and (3+1)-dimensional system of the time-fractional Navier–Stokes equations is gained by utilizing the triple-generalized Laplace transform decomposition method (TGLTDM) and quadruple-generalized Laplace transform decomposition method (FGLTDM). In addition, the results of the offered methods match with the exact solutions of the problems, which proves that, as the terms of the series increase, the approximate solutions are closer to the exact solutions of each problem. To verify the appropriateness of these methods, some examples are offered. The TGLTDM and FGLTDM results indicate that the suggested methods have higher evaluation convergence as compared to the ADM and HPM.

Keywords

• triple-generalized Laplace transform
• inverse triple-generalized Laplace transform
• quadruple-generalized Laplace transform
• fractional Navier–Stokes equation
• decomposition methods