Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
A new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in term...
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023414?viewType=HTML |
| _version_ | 1797905387706384384 |
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| author | Aziz Ur Rehman Muhammad Bilal Riaz Ilyas Khan Abdullah Mohamed |
| author_facet | Aziz Ur Rehman Muhammad Bilal Riaz Ilyas Khan Abdullah Mohamed |
| author_sort | Aziz Ur Rehman |
| collection | DOAJ |
| description | A new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on the newly introduced Constant Proportional Caputo fractional derivative operator. This fractional model has been solved analytically, and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. For the physical significance of various system parameters such as α, β, Pr, Gr, Gm, Sc on velocity, temperature and concentration profiles, different graphs are demonstrated by Mathcad software. The Constant Proportional Caputo fractional parameter exhibited a retardation effect on momentum and energy profile, but it is visualized that for small values of Casson fluid parameter, the velocity profile is higher. Furthermore, to validated the acquired solutions, some limiting models such as the ordinary Newtonian model are recovered from the fractionalized model. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, from the literature, it is observed that to deriving analytical results from fractional fluid models developed by the various fractional operators is difficult, and this article contributes to answering the open problem of obtaining analytical solutions for the fractionalized fluid models. |
| first_indexed | 2024-04-10T10:05:34Z |
| format | Article |
| id | doaj.art-4fa839e88d904cc49d640e5959631b1f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T10:05:34Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-4fa839e88d904cc49d640e5959631b1f2023-02-16T01:05:53ZengAIMS PressAIMS Mathematics2473-69882023-02-01848185820910.3934/math.2023414Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operatorAziz Ur Rehman 0Muhammad Bilal Riaz 1Ilyas Khan2Abdullah Mohamed31. Department of Mathematics, University of Management and Technology Lahore, Pakistan1. Department of Mathematics, University of Management and Technology Lahore, Pakistan 2. Faculty of Applied Physics and Mathematics, Gdansk University of Technology, 80-233 Gdansk, Poland3. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia4. Research Centre, Future University in Egypt, New Cairo 11835, EgyptA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on the newly introduced Constant Proportional Caputo fractional derivative operator. This fractional model has been solved analytically, and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. For the physical significance of various system parameters such as α, β, Pr, Gr, Gm, Sc on velocity, temperature and concentration profiles, different graphs are demonstrated by Mathcad software. The Constant Proportional Caputo fractional parameter exhibited a retardation effect on momentum and energy profile, but it is visualized that for small values of Casson fluid parameter, the velocity profile is higher. Furthermore, to validated the acquired solutions, some limiting models such as the ordinary Newtonian model are recovered from the fractionalized model. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, from the literature, it is observed that to deriving analytical results from fractional fluid models developed by the various fractional operators is difficult, and this article contributes to answering the open problem of obtaining analytical solutions for the fractionalized fluid models.https://www.aimspress.com/article/doi/10.3934/math.2023414?viewType=HTMLcpc derivativeanalytical solutionspecial functionssystem parameters |
| spellingShingle | Aziz Ur Rehman Muhammad Bilal Riaz Ilyas Khan Abdullah Mohamed Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator AIMS Mathematics cpc derivative analytical solution special functions system parameters |
| title | Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator |
| title_full | Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator |
| title_fullStr | Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator |
| title_full_unstemmed | Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator |
| title_short | Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator |
| title_sort | time fractional analysis of casson fluid with application of novel hybrid fractional derivative operator |
| topic | cpc derivative analytical solution special functions system parameters |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023414?viewType=HTML |
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