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

Abdelkader Moumen; Ramsha Shafqat; Azmat Ullah Khan Niazi; Nuttapol Pakkaranang; Mdi Begum Jeelani; Kiran Saleem; Abdelkader Moumen; Ramsha Shafqat; Azmat Ullah Khan Niazi; Nuttapol Pakkaranang; Mdi Begum Jeelani; Kiran Saleem

doi:10.3934/math.2023437

AIMS Mathematics

2023, Volume 8, Issue 4: 8702-8730. doi: 10.3934/math.2023437

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

1.
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
2.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
3.
Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 13314, Saudi Arabia

Received: 29 September 2022 Revised: 31 December 2022 Accepted: 10 January 2023 Published: 07 February 2023
MSC : 34A07, 34A08, 60G22

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.
- Navier-Stokes equations,
- mild solution,
- existence and uniqueness,
- Caputo fractional derivative,
- Mittag-Leffler functions,
- regularity
Citation: Abdelkader Moumen, Ramsha Shafqat, Azmat Ullah Khan Niazi, Nuttapol Pakkaranang, Mdi Begum Jeelani, Kiran Saleem. A study of the time fractional Navier-Stokes equations for vertical flow[J]. AIMS Mathematics, 2023, 8(4): 8702-8730. doi: 10.3934/math.2023437

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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.

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