Mittag-Leffler stability for a Timoshenko problem
A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of...
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| Format: | Article |
| Language: | English |
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Sciendo
2021-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.34768/amcs-2021-0015 |
| _version_ | 1819290880807272448 |
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| author | Tatar Nasser-Eddine |
| author_facet | Tatar Nasser-Eddine |
| author_sort | Tatar Nasser-Eddine |
| collection | DOAJ |
| description | A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero. |
| first_indexed | 2024-12-24T03:29:47Z |
| format | Article |
| id | doaj.art-ce4c996286724e58b4945765b3cd10cc |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-24T03:29:47Z |
| publishDate | 2021-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-ce4c996286724e58b4945765b3cd10cc2022-12-21T17:17:15ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922021-06-0131221923210.34768/amcs-2021-0015Mittag-Leffler stability for a Timoshenko problemTatar Nasser-Eddine0Department of Mathematics and Statistics, King Fahd University of Petroleum and MineralsDhahran31261, Saudi ArabiaA Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.https://doi.org/10.34768/amcs-2021-0015caputo fractional derivativemittag-leffler stabilitymultiplier techniqueresolvent operator |
| spellingShingle | Tatar Nasser-Eddine Mittag-Leffler stability for a Timoshenko problem International Journal of Applied Mathematics and Computer Science caputo fractional derivative mittag-leffler stability multiplier technique resolvent operator |
| title | Mittag-Leffler stability for a Timoshenko problem |
| title_full | Mittag-Leffler stability for a Timoshenko problem |
| title_fullStr | Mittag-Leffler stability for a Timoshenko problem |
| title_full_unstemmed | Mittag-Leffler stability for a Timoshenko problem |
| title_short | Mittag-Leffler stability for a Timoshenko problem |
| title_sort | mittag leffler stability for a timoshenko problem |
| topic | caputo fractional derivative mittag-leffler stability multiplier technique resolvent operator |
| url | https://doi.org/10.34768/amcs-2021-0015 |
| work_keys_str_mv | AT tatarnassereddine mittaglefflerstabilityforatimoshenkoproblem |