Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport
Abstract The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model $${\partial _{{t}} {\rho (x,t)}} = {\partial...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-06-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-63579-7 |
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| author | Anis Allagui Georgii Paradezhenko Anastasiia Pervishko Dmitry Yudin Hachemi Benaoum |
| author_facet | Anis Allagui Georgii Paradezhenko Anastasiia Pervishko Dmitry Yudin Hachemi Benaoum |
| author_sort | Anis Allagui |
| collection | DOAJ |
| description | Abstract The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model $${\partial _{{t}} {\rho (x,t)}} = {\partial ^2_{{x}} {\rho (x,t)}} - { \rho (x,t)}$$ ∂ t ρ ( x , t ) = ∂ x 2 ρ ( x , t ) - ρ ( x , t ) (also known as the Debye–Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order $$0<\alpha < 1$$ 0 < α < 1 , and the second-order space derivative with the Riesz-Feller fractional derivative of order $$0< \beta <2$$ 0 < β < 2 . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox’s H-function that we evaluate for different values of $$\alpha$$ α and $$\beta$$ β . |
| format | Article |
| id | doaj-art-ec4b966830ee49d9b3d2fcb546f8ca79 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-ec4b966830ee49d9b3d2fcb546f8ca792025-01-12T12:25:14ZengNature PortfolioScientific Reports2045-23222024-06-0114111010.1038/s41598-024-63579-7Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transportAnis Allagui0Georgii Paradezhenko1Anastasiia Pervishko2Dmitry Yudin3Hachemi Benaoum4Department of Sustainable and Renewable Energy Engineering, University of SharjahSkolkovo Institute of Science and TechnologySkolkovo Institute of Science and TechnologySkolkovo Institute of Science and TechnologyDepartment of Applied Physics and Astronomy, University of SharjahAbstract The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model $${\partial _{{t}} {\rho (x,t)}} = {\partial ^2_{{x}} {\rho (x,t)}} - { \rho (x,t)}$$ ∂ t ρ ( x , t ) = ∂ x 2 ρ ( x , t ) - ρ ( x , t ) (also known as the Debye–Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order $$0<\alpha < 1$$ 0 < α < 1 , and the second-order space derivative with the Riesz-Feller fractional derivative of order $$0< \beta <2$$ 0 < β < 2 . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox’s H-function that we evaluate for different values of $$\alpha$$ α and $$\beta$$ β .https://doi.org/10.1038/s41598-024-63579-7 |
| spellingShingle | Anis Allagui Georgii Paradezhenko Anastasiia Pervishko Dmitry Yudin Hachemi Benaoum Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport Scientific Reports |
| title | Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport |
| title_full | Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport |
| title_fullStr | Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport |
| title_full_unstemmed | Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport |
| title_short | Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport |
| title_sort | fundamental solution of the time space bi fractional diffusion equation with a kinetic source term for anomalous transport |
| url | https://doi.org/10.1038/s41598-024-63579-7 |
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