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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016820303690 |
| _version_ | 1818672966167166976 |
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| author | Naeem Faraz Yasir Khan Amna Anjum |
| author_facet | Naeem Faraz Yasir Khan Amna Anjum |
| author_sort | Naeem Faraz |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-17T07:48:17Z |
| format | Article |
| id | doaj.art-925bf98d59894c78abf727e557df6099 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-17T07:48:17Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-925bf98d59894c78abf727e557df60992022-12-21T21:57:55ZengElsevierAlexandria 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 |
| 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 |
| title | 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_short | Mathematical modelling of unsteady fractional Phan Thien Tanner fluid |
| title_sort | mathematical modelling of unsteady fractional phan thien tanner fluid |
| 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 |