In this study, numerical results of a fractional-order multi-dimensional model of the Navier–Stokes equations will be achieved via adoption of two analytical methods, i.e., the Adomian decomposition transform method and the q-Homotopy analysis transform method. The Caputo–Fabrizio operator will be used to define the fractional derivative. The proposed methods will be implemented to provide the series form results of the given models. The series form results of proposed techniques will be validated with the exact results available in the literature. The proposed techniques will be investigated to be efficient, straightforward, and reliable for application to many other scientific and engineering problems.