Abstract
This paper presents a new method that is constructed by combining the Shehu transform and the residual power series method. Precisely, we provide the application of the proposed technique to investigate fractional-order linear and nonlinear problems. Then, we implemented this new technique to obtain the result of fractional-order Navier-Stokes equations. Finally, we provide three-dimensional figures to help the effect of fractional derivatives on the actions of the achieved profile results on the proposed models.