Manoj Singh
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, 45142, Jazan, Kingdom of Saudi Arabia.

Mohammad Tamsir
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, 45142, Jazan, Kingdom of Saudi Arabia.

Yasser Salah El Saman
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, 45142, Jazan, Kingdom of Saudi Arabia.

Sarita Pundhir
Department of Mathematics, Delhi Technical Campus, Greater Noida, India.

DOI https://doi.org/10.33889/IJMEMS.2024.9.3.033

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Abstract

This article addresses the two analytical methods, i.e., the new iterative transform method (NITM) and the homotopy perturbation transform method (HPTM), along with an Aboodh transform (AT), to approximate the nonlinear system of two-dimensional (2D) time-fractional Navier-Stokes (TFNS) equations. We take the time-fractional derivative in the form of Atangana-Baleanu (AB). The article's suggested examples examine the accuracy and efficacy of the proposed methods, while the graphs demonstrate their potential and effectiveness. The article also provides demonstrations of uniqueness and convergence. The aforementioned techniques are straightforward and support a high rate of convergence, which helps in understanding the dynamics of fractional nonlinear systems.

Keywords- 2D-TFNS equations, NITM, HPTM, Integral transform, AB fractional derivative.

Citation

Singh, M., Tamsir, M., El Saman, Y. S. & Pundhir, S. (2024). Approximation of Two-Dimensional Time-Fractional Navier-Stokes Equations involving Atangana-Baleanu Derivative. International Journal of Mathematical, Engineering and Management Sciences, 9(3), 646-667. https://doi.org/10.33889/IJMEMS.2024.9.3.033.