One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations
This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation theorems are quite different from the corresp...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000608 |
| _version_ | 1797390329346785280 |
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| author | Muhammad Afdal Bau Mawardi Bahri Nasrullah Bachtiar St. Nurhilmah Busrah Muh. Nur |
| author_facet | Muhammad Afdal Bau Mawardi Bahri Nasrullah Bachtiar St. Nurhilmah Busrah Muh. Nur |
| author_sort | Muhammad Afdal Bau |
| collection | DOAJ |
| description | This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation theorems are quite different from the corresponding properties of the classical Laplace transform. Other properties like linearity, shifting, scaling and derivative are also studied in detail. Finally, the utility of the quaternion Laplace transform for solving quaternion-valued differential equations is presented. |
| first_indexed | 2024-03-08T23:10:10Z |
| format | Article |
| id | doaj.art-23106072f37443c08eb5d4cf3a7d59d1 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:10Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-23106072f37443c08eb5d4cf3a7d59d12023-12-15T07:26:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100547One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equationsMuhammad Afdal Bau0Mawardi Bahri1Nasrullah Bachtiar2St. Nurhilmah Busrah3Muh. Nur4Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, Indonesia; Corresponding author.Actuarial Science, Department of Science, Institut Teknologi Bacharuddin Jusuf Habibie, Pare-Pare 91121, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaThis paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation theorems are quite different from the corresponding properties of the classical Laplace transform. Other properties like linearity, shifting, scaling and derivative are also studied in detail. Finally, the utility of the quaternion Laplace transform for solving quaternion-valued differential equations is presented.http://www.sciencedirect.com/science/article/pii/S2666818123000608Quaternion algebraLaplace transformQuaternion Laplace transform |
| spellingShingle | Muhammad Afdal Bau Mawardi Bahri Nasrullah Bachtiar St. Nurhilmah Busrah Muh. Nur One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations Partial Differential Equations in Applied Mathematics Quaternion algebra Laplace transform Quaternion Laplace transform |
| title | One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations |
| title_full | One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations |
| title_fullStr | One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations |
| title_full_unstemmed | One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations |
| title_short | One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations |
| title_sort | one dimensional quaternion laplace transform properties and its application to quaternion valued differential equations |
| topic | Quaternion algebra Laplace transform Quaternion Laplace transform |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000608 |
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