An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics
The Laplace-Sumudu-Elzaki Transformation (LSET) represents a significant advancement in mathematical physics, offering versatile tools for solving differential equations and analyzing complex systems. This article provides a comprehensive introduction to LSET and explores its diverse applications in...
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10539364/ |
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| author | Qike Li Wei Wang |
| author_facet | Qike Li Wei Wang |
| author_sort | Qike Li |
| collection | DOAJ |
| description | The Laplace-Sumudu-Elzaki Transformation (LSET) represents a significant advancement in mathematical physics, offering versatile tools for solving differential equations and analyzing complex systems. This article provides a comprehensive introduction to LSET and explores its diverse applications in the realm of mathematical physics. Beginning with an overview of the fundamental principles and properties of the Laplace, Sumudu, and Elzaki transformations, we focus on their comparative analysis and elucidate their interrelations. Emphasizing the practical significance of these transformations, we discuss their applications in solving ordinary and partial differential equations, integral equations, delay differential equations, and fractional calculus problems. We investigate numerical techniques and algorithms for computing LSET, including implementation examples using popular software packages. We examine recent developments, emerging trends, and future directions in LSET research. Through case studies and illustrative examples, we demonstrate the efficacy of LSET in addressing real-world challenges across various domains of mathematical physics. This article serves as a valuable resource for researchers, practitioners, and students interested in harnessing the power of LSET to unravel complex phenomena and advance scientific knowledge. |
| format | Article |
| id | doaj-art-7356b4926a8446728be1686fa1ef16f2 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-7356b4926a8446728be1686fa1ef16f22024-12-21T00:01:43ZengIEEEIEEE Access2169-35362024-01-011218825618826610.1109/ACCESS.2024.340579110539364An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical PhysicsQike Li0https://orcid.org/0009-0009-4551-6338Wei Wang1School of General Education, Nantong Institute of Technology, Nantong, ChinaSchool of General Education, Nantong Institute of Technology, Nantong, ChinaThe Laplace-Sumudu-Elzaki Transformation (LSET) represents a significant advancement in mathematical physics, offering versatile tools for solving differential equations and analyzing complex systems. This article provides a comprehensive introduction to LSET and explores its diverse applications in the realm of mathematical physics. Beginning with an overview of the fundamental principles and properties of the Laplace, Sumudu, and Elzaki transformations, we focus on their comparative analysis and elucidate their interrelations. Emphasizing the practical significance of these transformations, we discuss their applications in solving ordinary and partial differential equations, integral equations, delay differential equations, and fractional calculus problems. We investigate numerical techniques and algorithms for computing LSET, including implementation examples using popular software packages. We examine recent developments, emerging trends, and future directions in LSET research. Through case studies and illustrative examples, we demonstrate the efficacy of LSET in addressing real-world challenges across various domains of mathematical physics. This article serves as a valuable resource for researchers, practitioners, and students interested in harnessing the power of LSET to unravel complex phenomena and advance scientific knowledge.https://ieeexplore.ieee.org/document/10539364/Laplace transformSumudu transformElzaki transformmathematical physicsdifferential equations |
| spellingShingle | Qike Li Wei Wang An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics IEEE Access Laplace transform Sumudu transform Elzaki transform mathematical physics differential equations |
| title | An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics |
| title_full | An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics |
| title_fullStr | An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics |
| title_full_unstemmed | An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics |
| title_short | An Introduction to the Laplace-Sumudu-Elzaki Transformation and Its Applications in Mathematical Physics |
| title_sort | introduction to the laplace sumudu elzaki transformation and its applications in mathematical physics |
| topic | Laplace transform Sumudu transform Elzaki transform mathematical physics differential equations |
| url | https://ieeexplore.ieee.org/document/10539364/ |
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