Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay
This paper analyzes an Euler-Bernoulli beam equation in a bounded domain with a boundary control condition involving a fractional derivative. By utilizing the semigroup theory of linear operators and building on the results of Borichev and Tomilov, the stability properties of the system are examined...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241541?viewType=HTML |
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| author | Boumediene Boukhari Foued Mtiri Ahmed Bchatnia Abderrahmane Beniani |
| author_facet | Boumediene Boukhari Foued Mtiri Ahmed Bchatnia Abderrahmane Beniani |
| author_sort | Boumediene Boukhari |
| collection | DOAJ |
| description | This paper analyzes an Euler-Bernoulli beam equation in a bounded domain with a boundary control condition involving a fractional derivative. By utilizing the semigroup theory of linear operators and building on the results of Borichev and Tomilov, the stability properties of the system are examined. Additionally, a numerical scheme is developed to reproduce various decay rate behaviors. The numerical simulations confirm the theoretical stability results regarding the energy decay rate and demonstrate exponential decay for specific configurations of initial data. |
| format | Article |
| id | doaj-art-cd80e17e5c1d4e1d918a43746b4924f7 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-cd80e17e5c1d4e1d918a43746b4924f72024-11-26T01:04:25ZengAIMS PressAIMS Mathematics2473-69882024-11-01911321023212310.3934/math.20241541Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decayBoumediene Boukhari 0Foued Mtiri1Ahmed Bchatnia 2Abderrahmane Beniani31. Department of Mathematics, Faculty of Science and Technology, Engineering and Sustainable Development Laboratory, University of Ain Temouchent, Ain Témouchent, 46000, Algeria2. Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha, Saudi Arabia3. Department of Mathematics, Faculty of Sciences of Tunis, LR Analyse Non-Linéaire et Géométrie, LR21ES08, University of Tunis El Manar, Tunis, 2092, Tunisia1. Department of Mathematics, Faculty of Science and Technology, Engineering and Sustainable Development Laboratory, University of Ain Temouchent, Ain Témouchent, 46000, AlgeriaThis paper analyzes an Euler-Bernoulli beam equation in a bounded domain with a boundary control condition involving a fractional derivative. By utilizing the semigroup theory of linear operators and building on the results of Borichev and Tomilov, the stability properties of the system are examined. Additionally, a numerical scheme is developed to reproduce various decay rate behaviors. The numerical simulations confirm the theoretical stability results regarding the energy decay rate and demonstrate exponential decay for specific configurations of initial data.https://www.aimspress.com/article/doi/10.3934/math.20241541?viewType=HTMLeuler-bernoulli beam equationdynamic boundary dissipation of fractional derivative typefrequency domain methodstrong stability |
| spellingShingle | Boumediene Boukhari Foued Mtiri Ahmed Bchatnia Abderrahmane Beniani Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay AIMS Mathematics euler-bernoulli beam equation dynamic boundary dissipation of fractional derivative type frequency domain method strong stability |
| title | Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay |
| title_full | Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay |
| title_fullStr | Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay |
| title_full_unstemmed | Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay |
| title_short | Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay |
| title_sort | fractional derivative boundary control in coupled euler bernoulli beams stability and discrete energy decay |
| topic | euler-bernoulli beam equation dynamic boundary dissipation of fractional derivative type frequency domain method strong stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241541?viewType=HTML |
| work_keys_str_mv | AT boumedieneboukhari fractionalderivativeboundarycontrolincoupledeulerbernoullibeamsstabilityanddiscreteenergydecay AT fouedmtiri fractionalderivativeboundarycontrolincoupledeulerbernoullibeamsstabilityanddiscreteenergydecay AT ahmedbchatnia fractionalderivativeboundarycontrolincoupledeulerbernoullibeamsstabilityanddiscreteenergydecay AT abderrahmanebeniani fractionalderivativeboundarycontrolincoupledeulerbernoullibeamsstabilityanddiscreteenergydecay |