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This article arrangement with N-S equation containing the Caputo-Fabrizio differential operator of fractional order. The Iterative Laplace Transform Method (ILTM) has been applied to found numerical solution of time-fractional N-S equation in a tube with unsteady fluid flow in the Caputo-Fabrizio sense. The ILTM is an elegant coupling of transform of the Laplace and new Iterative method (NIM). This scheme provides numerical solution in the terms of power series with easily computable terms. It is observed that the solutions of N-S equations obtained by the ILTM rapidly convergent to exact solutions.

In this article, a hybrid method called iteration Shehu transform method has been implemented to solve fractional-order NavierâStokes equation. Atangana-Balenu operator describes fractional-order derivatives. The analytical solutions of three distinct examples of the time-fractional Navier-Stokes equations are determined by using Iterative shehu transform method. Further, we present the eectiveness and accuracy of the proposed method by comparison of analytical solutions to the exact solutions and the results are represented graphically and numerically.

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