A new efficient technique using Laplace transforms and smooth expansions to construct a series solution to the time-fractional Navier-Stokes equations

Abstract

In this article, we introduce a new technique to create a series solution to the time-fractional Navier - Stokes equations is using a combination of the Laplace Transform with the residual power series method. Laurent series presented in the construction of the proposed method used for solving fractional physical equations. Speed and accuracy in extracting an exact or approximate solution are the most features of the new procedure. The proposed method examined two Navier-Stokes equations that representing the motion of flow in a pipe. Comparisons with previous methods and error analysis were performed to demonstrate the efficacy and accuracy of the technique.

Keywords

• Series solutions
• Caputo fractional derivative
• Fractional partial differential equations
• Integral transforms