Mathematical modelling of unsteady fractional Phan Thien Tanner fluid

Mathematical modelling of unsteady fractional Phan Thien Tanner fluid

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. For the first time, unsteady fractional Phan Thien Tanner fluid is modeled, which results in different space-time nonlinear fractional partial differential equations. All obtained fractional...

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Main Authors: Naeem Faraz, Yasir Khan, Amna Anjum
Format: Article
Language:English
Published: Elsevier 2020-12-01
Series:Alexandria Engineering Journal
Subjects:
Phan-Thein-Tanner (PTT) model
Fractional
Nonlinear
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016820303690
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spelling doaj-925bf98d59894c78abf727e557df60992021-06-02T19:59:45ZengElsevierAlexandria Engineering Journal1110-01682020-12-0159643914395Mathematical modelling of unsteady fractional Phan Thien Tanner fluidNaeem Faraz0Yasir Khan1Amna Anjum2International Cultural Exchange School (ICES), Donghua University, West Yanan Road 1882, Shanghai 200051, China; Corresponding author.Department of Mathematics, University of Hafr Al-Batin, 31991, Saudi ArabiaInternational Cultural Exchange School (ICES), Donghua University, West Yanan Road 1882, Shanghai 200051, China; Glorious Sun School of Business and Management, Donghua University, West Yan’an Road 1882, Shanghai 200051, ChinaThe fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. For the first time, unsteady fractional Phan Thien Tanner fluid is modeled, which results in different space-time nonlinear fractional partial differential equations. All obtained fractional differential equations models have never been reported before in the literature. These mathematical models have been modeled by using the Mittag Leffler function, which helps to deduce some individual cases. Readers can use any analytical or numerical method to solve the modeled fractional differential equations.http://www.sciencedirect.com/science/article/pii/S1110016820303690Phan-Thein-Tanner (PTT) modelFractionalNonlinear
collection DOAJ
language English
format Article
sources DOAJ
author Naeem Faraz
Yasir Khan
Amna Anjum
spellingShingle Naeem Faraz
Yasir Khan
Amna Anjum
Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
Alexandria Engineering Journal
Phan-Thein-Tanner (PTT) model
Fractional
Nonlinear
author_facet Naeem Faraz
Yasir Khan
Amna Anjum
author_sort Naeem Faraz
title Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
title_short Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
title_full Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
title_fullStr Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
title_full_unstemmed Mathematical modelling of unsteady fractional Phan Thien Tanner fluid
title_sort mathematical modelling of unsteady fractional phan thien tanner fluid
publisher Elsevier
series Alexandria Engineering Journal
issn 1110-0168
publishDate 2020-12-01
description The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. For the first time, unsteady fractional Phan Thien Tanner fluid is modeled, which results in different space-time nonlinear fractional partial differential equations. All obtained fractional differential equations models have never been reported before in the literature. These mathematical models have been modeled by using the Mittag Leffler function, which helps to deduce some individual cases. Readers can use any analytical or numerical method to solve the modeled fractional differential equations.
topic Phan-Thein-Tanner (PTT) model
Fractional
Nonlinear
url http://www.sciencedirect.com/science/article/pii/S1110016820303690
work_keys_str_mv AT naeemfaraz mathematicalmodellingofunsteadyfractionalphanthientannerfluid
AT yasirkhan mathematicalmodellingofunsteadyfractionalphanthientannerfluid
AT amnaanjum mathematicalmodellingofunsteadyfractionalphanthientannerfluid
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