Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative
A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation...
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MDPI AG
2021-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/9/4142 |
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| author | Nehad Ali Shah Abdul Rauf Dumitru Vieru Kanokwan Sitthithakerngkiet Poom Kumam |
| author_facet | Nehad Ali Shah Abdul Rauf Dumitru Vieru Kanokwan Sitthithakerngkiet Poom Kumam |
| author_sort | Nehad Ali Shah |
| collection | DOAJ |
| description | A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad. |
| first_indexed | 2024-03-10T11:46:44Z |
| format | Article |
| id | doaj.art-eadd64d3b49d47dcb5d580647db75131 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T11:46:44Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-eadd64d3b49d47dcb5d580647db751312023-11-21T18:02:51ZengMDPI AGApplied Sciences2076-34172021-04-01119414210.3390/app11094142Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional DerivativeNehad Ali Shah0Abdul Rauf1Dumitru Vieru2Kanokwan Sitthithakerngkiet3Poom Kumam4Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, VietnamDepartment of Computer Science and Mathematics, Air University Multan Campus, Multan 60000, PakistanDepartment of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, RomaniaIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok 10140, ThailandDepartments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandA generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad.https://www.mdpi.com/2076-3417/11/9/4142radial diffusion–wave equationfractional derivativedistributed-orderintegral transforms |
| spellingShingle | Nehad Ali Shah Abdul Rauf Dumitru Vieru Kanokwan Sitthithakerngkiet Poom Kumam Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative Applied Sciences radial diffusion–wave equation fractional derivative distributed-order integral transforms |
| title | Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative |
| title_full | Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative |
| title_fullStr | Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative |
| title_full_unstemmed | Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative |
| title_short | Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative |
| title_sort | analytical solutions of the diffusion wave equation of groundwater flow with distributed order of atangana baleanu fractional derivative |
| topic | radial diffusion–wave equation fractional derivative distributed-order integral transforms |
| url | https://www.mdpi.com/2076-3417/11/9/4142 |
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