Approximate Solution for The Nonlinear Fractional Coupled Navier–Stokes of The Fluid Model of 2−Dimensional by Using A Hybrid Technique

The current paper investigates the fractional Navier–Stokes of the fluid model in which the differential is of non-integer order. In addition, some basic definitions are discussed. This research aims to find an approximate solution to non-linear Fractional Coupled Navier–Stokes Equation (FCNSE) in two-dimension by using a hybrid technique. Thus, we propose a hybrid the Shehu transform (S-transform) with the homotopy perturbation method to solve this model. The S-transform with homotopy perturbation is an excellent combination in applied mathematics and engineering that permits in converting FCNSE into algebraic equations . Then, through solving this algebraic equation, it is possible to obtain the unknown function utilizing some modifications with the help of inverse S- transform. For demonstrating the effectiveness and capabilities of the proposed innovation, various illustrative examples were applied.