Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line
The fractional Bagley-Torvik system (FBTS) is initially created by utilizing fractional calculus to study the demeanor of real materials. It can be described as the dynamics of an inflexible plate dipped in a Newtonian fluid. In the present article, we aim for the first time to discuss the existence...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024246?viewType=HTML |
| _version_ | 1797322547767803904 |
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| author | Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez |
| author_facet | Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez |
| author_sort | Sabri T. M. Thabet |
| collection | DOAJ |
| description | The fractional Bagley-Torvik system (FBTS) is initially created by utilizing fractional calculus to study the demeanor of real materials. It can be described as the dynamics of an inflexible plate dipped in a Newtonian fluid. In the present article, we aim for the first time to discuss the existence and uniqueness (E&U) theories of an unbounded solution for the proposed generalized FBTS involving Riemann-Liouville fractional derivatives in the half-line $ (0, \infty) $, by using fixed point theorems (FPTs). Moreover, the Hyers-Ulam stability (HUS), Hyers-Ulam-Rassias stability (HURS), and semi-Hyers-Ulam-Rassias stability (sHURS) are proved. Finally, two numerical examples are given for checking the validity of major findings. By investigating unbounded solutions for the FBTS, engineers gain a deeper understanding of the underlying physics, optimize performance, improve system design, and ensure the stability of the motion of real materials in a Newtonian fluid. |
| first_indexed | 2024-03-08T05:14:54Z |
| format | Article |
| id | doaj.art-3704990b69a94033b63409d287c52119 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:14:54Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3704990b69a94033b63409d287c521192024-02-07T01:29:28ZengAIMS PressAIMS Mathematics2473-69882024-01-01925071508710.3934/math.2024246Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-lineSabri T. M. Thabet 0Imed Kedim1Miguel Vivas-Cortez 21. Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen2. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia3. Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, EcuadorThe fractional Bagley-Torvik system (FBTS) is initially created by utilizing fractional calculus to study the demeanor of real materials. It can be described as the dynamics of an inflexible plate dipped in a Newtonian fluid. In the present article, we aim for the first time to discuss the existence and uniqueness (E&U) theories of an unbounded solution for the proposed generalized FBTS involving Riemann-Liouville fractional derivatives in the half-line $ (0, \infty) $, by using fixed point theorems (FPTs). Moreover, the Hyers-Ulam stability (HUS), Hyers-Ulam-Rassias stability (HURS), and semi-Hyers-Ulam-Rassias stability (sHURS) are proved. Finally, two numerical examples are given for checking the validity of major findings. By investigating unbounded solutions for the FBTS, engineers gain a deeper understanding of the underlying physics, optimize performance, improve system design, and ensure the stability of the motion of real materials in a Newtonian fluid.https://www.aimspress.com/article/doi/10.3934/math.2024246?viewType=HTMLfractional derivativesbagley-torvik equationfixed point theoremsunbounded solutions |
| spellingShingle | Sabri T. M. Thabet Imed Kedim Miguel Vivas-Cortez Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line AIMS Mathematics fractional derivatives bagley-torvik equation fixed point theorems unbounded solutions |
| title | Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line |
| title_full | Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line |
| title_fullStr | Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line |
| title_full_unstemmed | Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line |
| title_short | Efficient results on unbounded solutions of fractional Bagley-Torvik system on the half-line |
| title_sort | efficient results on unbounded solutions of fractional bagley torvik system on the half line |
| topic | fractional derivatives bagley-torvik equation fixed point theorems unbounded solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024246?viewType=HTML |
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