On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms
This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/7/514 |
| _version_ | 1797589240143413248 |
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| author | Said Mesloub Reem K. Alhefthi |
| author_facet | Said Mesloub Reem K. Alhefthi |
| author_sort | Said Mesloub |
| collection | DOAJ |
| description | This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method. |
| first_indexed | 2024-03-11T01:03:42Z |
| format | Article |
| id | doaj.art-7193fc2096b74aad9f1f089d55acdcab |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T01:03:42Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7193fc2096b74aad9f1f089d55acdcab2023-11-18T19:25:47ZengMDPI AGFractal and Fractional2504-31102023-06-017751410.3390/fractalfract7070514On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping TermsSaid Mesloub0Reem K. Alhefthi1Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaMathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThis paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method.https://www.mdpi.com/2504-3110/7/7/514fractional systemfrictional dampingnonlocala priori boundnonlocal conditionsingular system |
| spellingShingle | Said Mesloub Reem K. Alhefthi On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms Fractal and Fractional fractional system frictional damping nonlocal a priori bound nonlocal condition singular system |
| title | On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms |
| title_full | On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms |
| title_fullStr | On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms |
| title_full_unstemmed | On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms |
| title_short | On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms |
| title_sort | on a singular non local fractional system describing a generalized timoshenko system with two frictional damping terms |
| topic | fractional system frictional damping nonlocal a priori bound nonlocal condition singular system |
| url | https://www.mdpi.com/2504-3110/7/7/514 |
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