An analytical approach of multi-dimensional Navier-Stokes equation in the framework of natural transform

Manoj Singh; Ahmed Hussein; Msmali; Mohammad Tamsir; Abdullah Ali H. Ahmadini; Manoj Singh; Ahmed Hussein; Msmali; Mohammad Tamsir; Abdullah Ali H. Ahmadini

doi:10.3934/math.2024426

AIMS Mathematics

2024, Volume 9, Issue 4: 8776-8802. doi: 10.3934/math.2024426

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An analytical approach of multi-dimensional Navier-Stokes equation in the framework of natural transform

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
2.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, Australia

Received: 31 December 2023 Revised: 06 February 2024 Accepted: 21 February 2024 Published: 01 March 2024

This article introduces a new iterative transform method and homotopy perturbation transform method along with a natural transform to analyze the multi-dimensional Navier-Stokes equations. To solve the fractional-derivative, the Caputo-Fabrizio definition of the fractional derivative was employed. Four examples were considered to examine the efficacy and accuracy of the proposed methods. The efficiency and accuracy were also demonstrated by the solution comparison via graphs. The proposed methods' convergence and uniqueness are also discussed. The methods mentioned above are straightforward and support a high rate of convergence.
- Navier-Stokes equation,
- new iterative transform method,
- Homotopy perturbation transform method,
- natural transform,
- Caputo-Fabrizio fractional derivative
Citation: Manoj Singh, Ahmed Hussein, Msmali, Mohammad Tamsir, Abdullah Ali H. Ahmadini. An analytical approach of multi-dimensional Navier-Stokes equation in the framework of natural transform[J]. AIMS Mathematics, 2024, 9(4): 8776-8802. doi: 10.3934/math.2024426

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Abstract

This article introduces a new iterative transform method and homotopy perturbation transform method along with a natural transform to analyze the multi-dimensional Navier-Stokes equations. To solve the fractional-derivative, the Caputo-Fabrizio definition of the fractional derivative was employed. Four examples were considered to examine the efficacy and accuracy of the proposed methods. The efficiency and accuracy were also demonstrated by the solution comparison via graphs. The proposed methods' convergence and uniqueness are also discussed. The methods mentioned above are straightforward and support a high rate of convergence.

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