In this article, a new developed approach to solve multi-dimensional time-fractional Navier–Stokes equation resulting from the incompressible fluid flow is presented. Controlled Picard’s technique is merged with Laplace transform producing an elegant frame characteristic with its ability to solve nonlinear fractional equations, without the calculation of Lagrange multiplier or Adomian polynomial, and the presence of the small parameter , which reinforces the convergence and is convenient for nonlinear differential equations. The characteristic of this approach is its ability to combine two robust methods in the presence of the auxiliary parameter h for determining exact and approximate analytical solutions for nonlinear equations.