Y. Alkhezi - Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), Shuwaikh 70654, Kuwait. A. Shafee - PAAET, College of Technological Studies, Laboratory Technology Department, Shuwaikh 70654, Kuwait.
The present paper explores the use of the Mohand Variational Iteration Method (MVIM) and \(q\)-Homotopy Mohand Transform Method (\(q\)-HMTM) to get approximate analytical solutions of the Caputo-type of fractional Navier-Stokes equations. Adaptability of the two methods is evaluated using two different sets of initial conditions. The Mohand transformation allows the fractional derivatives to be treated easily and handle coupled nonlinear terms easily, while the \(q\)-HMTM adds an auxiliary parameter that comes to control the convergence of the series solution. Quantitative solutions given both in tables and graphs show that the solutions given by both procedures are in very good agreement with the exact solutions. Comparative analysis shows reliability, stability, and high accuracy of both MVIM and \(q\)-HMTM in solving nonlinear coupled fractional PDEs, and outlines the possibilities of the Mohand transformation as an efficient analytical method in fractional fluid dynamics.
Y. Alkhezi, A. Shafee, Algebraic approaches to solving fractional coupled Navier-Stokes equations, Journal of Mathematics and Computer Science, 42 (2026), no. 1, 64--84
Alkhezi Y., Shafee A., Algebraic approaches to solving fractional coupled Navier-Stokes equations. J Math Comput SCI-JM. (2026); 42(1):64--84
Alkhezi, Y., Shafee, A.. "Algebraic approaches to solving fractional coupled Navier-Stokes equations." Journal of Mathematics and Computer Science, 42, no. 1 (2026): 64--84
