Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations
In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt...
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2778 |
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| author | L. Chitra K. Alagesan Vediyappan Govindan Salman Saleem A. Al-Zubaidi C. Vimala |
| author_facet | L. Chitra K. Alagesan Vediyappan Govindan Salman Saleem A. Al-Zubaidi C. Vimala |
| author_sort | L. Chitra |
| collection | DOAJ |
| description | In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform. |
| first_indexed | 2024-03-11T02:11:03Z |
| format | Article |
| id | doaj.art-153925ff36b842b698cac1b9d9b5cfe1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:11:03Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-153925ff36b842b698cac1b9d9b5cfe12023-11-18T11:29:39ZengMDPI AGMathematics2227-73902023-06-011112277810.3390/math11122778Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential EquationsL. Chitra0K. Alagesan1Vediyappan Govindan2Salman Saleem3A. Al-Zubaidi4C. Vimala5Department of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, IndiaDepartment of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, IndiaDepartment of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam, Chennai 603103, Tamil Nadu, IndiaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Periyar Maniammai Institute of Science & Technology, Vallam, Thanjavur 613403, Tamil Nadu, IndiaIn this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform.https://www.mdpi.com/2227-7390/11/12/2778differential equationHyers–Ulam stability (HUS)Tarig transform |
| spellingShingle | L. Chitra K. Alagesan Vediyappan Govindan Salman Saleem A. Al-Zubaidi C. Vimala Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations Mathematics differential equation Hyers–Ulam stability (HUS) Tarig transform |
| title | Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations |
| title_full | Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations |
| title_fullStr | Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations |
| title_full_unstemmed | Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations |
| title_short | Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations |
| title_sort | applications of the tarig transform and hyers ulam stability to linear differential equations |
| topic | differential equation Hyers–Ulam stability (HUS) Tarig transform |
| url | https://www.mdpi.com/2227-7390/11/12/2778 |
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