Malaysian Journal of Mathematical Sciences, June 2025, Vol. 19, No. 2
Approximate Solution for The Nonlinear Fractional Coupled Navier—Stokes of The Fluid Model of $2-$Dimensional by Using A Hybrid Technique
Albuohimad, B., Saloomi, M. H., and Salman, M. R.
Corresponding Email: basim.albuohimad@uokerbala.edu.iq
Received date: 2 October 2024
Accepted date: 18 November 2024
Abstract:
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 ($\mathbb{S}$-transform) with the homotopy perturbation method to solve this model. The $\mathbb{S}$-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 $\mathbb{S}$- transform. For demonstrating the effectiveness and capabilities of the proposed innovation, various illustrative examples were applied.
Keywords: fractional calculus; homotopy perturbation method; Shehu transform; Navier—Stokes
