Algebraic methods for handling fractional coupled Equations of Navier-Stokes

Abstract

In order to get approximate analytical solutions to the Caputo-type of fractional Navier-Stokes equations, this study investigates the use of the Mohand Variational Iteration Method (MVIM) and the q-Homotopy Mohand Transform Method (q-HMTM). Two distinct sets of beginning circumstances are used to assess the adaptability of the two approaches. The q-HMTM adds an auxiliary parameter that comes to govern the convergence of the series solution, while the Mohand transformation makes it simple to handle coupled nonlinear components and deal fractional derivatives. The quantitative answers provided by both approaches are in extremely excellent agreement with the actual solutions, as shown by the tables and graphs. In solving nonlinear coupled fractional PDEs, comparative analysis demonstrates the excellent accuracy, stability, and dependability of both MVIM and q-HMTM. It also highlights the potential of the Mohand transformation as an effective analytical technique in fractional fluid dynamics.