Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study
This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) C F ( ∂ β / ∂ t β ) and Atangana–Baleanu (AB) A B ( ∂ α / ∂ t α ) fractiona...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/8/279 |
| _version_ | 1818001039926755328 |
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| author | Arshad Khan Kashif Ali Abro Asifa Tassaddiq Ilyas Khan |
| author_facet | Arshad Khan Kashif Ali Abro Asifa Tassaddiq Ilyas Khan |
| author_sort | Arshad Khan |
| collection | DOAJ |
| description | This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) C F ( ∂ β / ∂ t β ) and Atangana–Baleanu (AB) A B ( ∂ α / ∂ t α ) fractional derivatives. For this purpose, second grade fluids flow with combined gradients of mass concentration and temperature distribution over a vertical flat plate is considered. The problem is first written in non-dimensional form and then based on AB and CF fractional derivatives, it is developed in fractional form, and then using the Laplace transform technique, exact solutions are established for both cases of AB and CF derivatives. They are then expressed in terms of newly defined M-function M q p ( z ) and generalized Hyper-geometric function p Ψ q ( z ) . The obtained exact solutions are plotted graphically for several pertinent parameters and an interesting comparison is made between AB and CF derivatives results with various similarities and differences. |
| first_indexed | 2024-04-14T03:29:18Z |
| format | Article |
| id | doaj.art-aa17135a29b6462faafc2d66db79b2d9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T03:29:18Z |
| publishDate | 2017-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-aa17135a29b6462faafc2d66db79b2d92022-12-22T02:15:02ZengMDPI AGEntropy1099-43002017-08-0119827910.3390/e19080279e19080279Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative StudyArshad Khan0Kashif Ali Abro1Asifa Tassaddiq2Ilyas Khan3Department of Computer Science and IT, Sarhad University of Science and IT Peshawar, Peshawar 25000, PakistanDepartment of Basic Sciences and Related Studies, Mehran University of Engineering Technology, Jamshoro 76062, PakistanComputer Sciences and Information Technology College, Majmaah University Majmaah, Majmaah 11952, Saudi ArabiaBasic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952, Saudi ArabiaThis communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo–Mauro Fabrizio (CF) C F ( ∂ β / ∂ t β ) and Atangana–Baleanu (AB) A B ( ∂ α / ∂ t α ) fractional derivatives. For this purpose, second grade fluids flow with combined gradients of mass concentration and temperature distribution over a vertical flat plate is considered. The problem is first written in non-dimensional form and then based on AB and CF fractional derivatives, it is developed in fractional form, and then using the Laplace transform technique, exact solutions are established for both cases of AB and CF derivatives. They are then expressed in terms of newly defined M-function M q p ( z ) and generalized Hyper-geometric function p Ψ q ( z ) . The obtained exact solutions are plotted graphically for several pertinent parameters and an interesting comparison is made between AB and CF derivatives results with various similarities and differences.https://www.mdpi.com/1099-4300/19/8/279AB and CF derivativesM-function M q p ( z ) and generalized Hyper-geometric function p Ψ q ( z )convection flowheat and mass transferexact solutions |
| spellingShingle | Arshad Khan Kashif Ali Abro Asifa Tassaddiq Ilyas Khan Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study Entropy AB and CF derivatives M-function M q p ( z ) and generalized Hyper-geometric function p Ψ q ( z ) convection flow heat and mass transfer exact solutions |
| title | Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study |
| title_full | Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study |
| title_fullStr | Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study |
| title_full_unstemmed | Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study |
| title_short | Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study |
| title_sort | atangana baleanu and caputo fabrizio analysis of fractional derivatives for heat and mass transfer of second grade fluids over a vertical plate a comparative study |
| topic | AB and CF derivatives M-function M q p ( z ) and generalized Hyper-geometric function p Ψ q ( z ) convection flow heat and mass transfer exact solutions |
| url | https://www.mdpi.com/1099-4300/19/8/279 |
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