Time-Fractional Heat Conduction in Two Joint Half-Planes
The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace tran...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/6/800 |
| _version_ | 1798005654357540864 |
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| author | Yuriy Povstenko Joanna Klekot |
| author_facet | Yuriy Povstenko Joanna Klekot |
| author_sort | Yuriy Povstenko |
| collection | DOAJ |
| description | The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver−Stehfest method. We give a graphical representation of the numerical results. |
| first_indexed | 2024-04-11T12:42:46Z |
| format | Article |
| id | doaj.art-12ee91b8e127496bbfc78fc67cb737ec |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T12:42:46Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-12ee91b8e127496bbfc78fc67cb737ec2022-12-22T04:23:26ZengMDPI AGSymmetry2073-89942019-06-0111680010.3390/sym11060800sym11060800Time-Fractional Heat Conduction in Two Joint Half-PlanesYuriy Povstenko0Joanna Klekot1Institute of Mathematics and Computer Science, Faculty of Mathematical and Natural Sciences, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, PolandInstitute of Mathematics, Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology, Armii Krajowej 21, 42-200 Czestochowa, PolandThe heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver−Stehfest method. We give a graphical representation of the numerical results.https://www.mdpi.com/2073-8994/11/6/800fractional calculusnon-Fourier heat conductionCaputo derivativeFourier transformLaplace transform |
| spellingShingle | Yuriy Povstenko Joanna Klekot Time-Fractional Heat Conduction in Two Joint Half-Planes Symmetry fractional calculus non-Fourier heat conduction Caputo derivative Fourier transform Laplace transform |
| title | Time-Fractional Heat Conduction in Two Joint Half-Planes |
| title_full | Time-Fractional Heat Conduction in Two Joint Half-Planes |
| title_fullStr | Time-Fractional Heat Conduction in Two Joint Half-Planes |
| title_full_unstemmed | Time-Fractional Heat Conduction in Two Joint Half-Planes |
| title_short | Time-Fractional Heat Conduction in Two Joint Half-Planes |
| title_sort | time fractional heat conduction in two joint half planes |
| topic | fractional calculus non-Fourier heat conduction Caputo derivative Fourier transform Laplace transform |
| url | https://www.mdpi.com/2073-8994/11/6/800 |
| work_keys_str_mv | AT yuriypovstenko timefractionalheatconductionintwojointhalfplanes AT joannaklekot timefractionalheatconductionintwojointhalfplanes |