On fractional Pennes bio-heat equation using Legendre collocation method
In this paper, the distribution of heat in skin tissue during thermal treatment using the time-fractional Pennes model is studied. Temperature variations concerning several parameters such as derivative [Formula: see text] time, blood perfusion, and transmitted power are described using the Legendre...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500217 |
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| author | Arvind Kumar Mishra Sushil Kumar Ajay Kumar Shukla |
| author_facet | Arvind Kumar Mishra Sushil Kumar Ajay Kumar Shukla |
| author_sort | Arvind Kumar Mishra |
| collection | DOAJ |
| description | In this paper, the distribution of heat in skin tissue during thermal treatment using the time-fractional Pennes model is studied. Temperature variations concerning several parameters such as derivative [Formula: see text] time, blood perfusion, and transmitted power are described using the Legendre collocation technique. The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. The obtained results and comparison with an exact solution are illustrated. |
| format | Article |
| id | doaj-art-bb5da168a9604897882f4ff1fad8d9cb |
| institution | Kabale University |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-bb5da168a9604897882f4ff1fad8d9cb2025-01-31T06:15:28ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500217On fractional Pennes bio-heat equation using Legendre collocation methodArvind Kumar Mishra0Sushil Kumar1Ajay Kumar Shukla2Department of Mathematics, Thadomal Shahani Engineering College, Mumbai-400050, Maharashtra, IndiaDepartment of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat, IndiaDepartment of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat, IndiaIn this paper, the distribution of heat in skin tissue during thermal treatment using the time-fractional Pennes model is studied. Temperature variations concerning several parameters such as derivative [Formula: see text] time, blood perfusion, and transmitted power are described using the Legendre collocation technique. The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. The obtained results and comparison with an exact solution are illustrated.https://www.worldscientific.com/doi/10.1142/S2661335224500217Fractional bio-heat equationCaputo’s fractional derivativeShifted Legendre polynomialcollocation method |
| spellingShingle | Arvind Kumar Mishra Sushil Kumar Ajay Kumar Shukla On fractional Pennes bio-heat equation using Legendre collocation method International Journal of Mathematics for Industry Fractional bio-heat equation Caputo’s fractional derivative Shifted Legendre polynomial collocation method |
| title | On fractional Pennes bio-heat equation using Legendre collocation method |
| title_full | On fractional Pennes bio-heat equation using Legendre collocation method |
| title_fullStr | On fractional Pennes bio-heat equation using Legendre collocation method |
| title_full_unstemmed | On fractional Pennes bio-heat equation using Legendre collocation method |
| title_short | On fractional Pennes bio-heat equation using Legendre collocation method |
| title_sort | on fractional pennes bio heat equation using legendre collocation method |
| topic | Fractional bio-heat equation Caputo’s fractional derivative Shifted Legendre polynomial collocation method |
| url | https://www.worldscientific.com/doi/10.1142/S2661335224500217 |
| work_keys_str_mv | AT arvindkumarmishra onfractionalpennesbioheatequationusinglegendrecollocationmethod AT sushilkumar onfractionalpennesbioheatequationusinglegendrecollocationmethod AT ajaykumarshukla onfractionalpennesbioheatequationusinglegendrecollocationmethod |