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Research Article | Open Access

A study of the time fractional Navier-Stokes equations for vertical flow

Abdelkader Moumen1, Ramsha Shafqat2, Azmat Ullah Khan Niazi2, Nuttapol Pakkaranang3( ), Mdi Begum Jeelani4, Kiran Saleem2
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 13314, Saudi Arabia
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Abstract

Navier-Stokes (NS) equations dealing with gravitational force with time-fractional derivatives are discussed in this paper. These equations can be used to predict fluid velocity and pressure for a given geometry. This paper investigates the local and global existence and uniqueness of mild solutions to NS equations for the time fractional differential operator. We also work on the regularity effects of such types of equations were caused by orthogonal flow.

Keywords

Navier-Stokes equationsmild solutionexistence and uniquenessCaputo fractional derivativeMittag-Leffler functionsregularity
CLC number: 34A07, 34A08, 60G22

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 8702-8730
DOI: 10.3934/math.2023437

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Cite this article:
Moumen A, Shafqat R, Niazi AUK, et al. A study of the time fractional Navier-Stokes equations for vertical flow. AIMS Mathematics, 2023, 8(4): 8702-8730. https://doi.org/10.3934/math.2023437

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Received: 29 September 2022
Revised: 31 December 2022
Accepted: 10 January 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)