The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provid...
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| Format: | Article |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/353 |
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| author | Hanaa Zitane Ali Boutoulout Delfim F. M. Torres |
| author_facet | Hanaa Zitane Ali Boutoulout Delfim F. M. Torres |
| author_sort | Hanaa Zitane |
| collection | DOAJ |
| description | We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics are symmetric and uniformly elliptical and by using the properties of the Mittag−Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results. |
| first_indexed | 2024-12-11T20:28:03Z |
| format | Article |
| id | doaj.art-c118ee0b869c42ebb8301a40d0b63a42 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T20:28:03Z |
| publishDate | 2020-03-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c118ee0b869c42ebb8301a40d0b63a422022-12-22T00:51:55ZengMDPI AGMathematics2227-73902020-03-018335310.3390/math8030353math8030353The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear SystemsHanaa Zitane0Ali Boutoulout1Delfim F. M. Torres2MACS Laboratory, Department of Mathematics, Faculty of Sciences, University of Moulay Ismail, 11201 Meknes, MoroccoMACS Laboratory, Department of Mathematics, Faculty of Sciences, University of Moulay Ismail, 11201 Meknes, MoroccoCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalWe investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics are symmetric and uniformly elliptical and by using the properties of the Mittag−Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.https://www.mdpi.com/2227-7390/8/3/353fractional differential equationsfractional diffusion systemscaputo derivativestability and stabilization in hilbert spacesdecomposition method |
| spellingShingle | Hanaa Zitane Ali Boutoulout Delfim F. M. Torres The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems Mathematics fractional differential equations fractional diffusion systems caputo derivative stability and stabilization in hilbert spaces decomposition method |
| title | The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems |
| title_full | The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems |
| title_fullStr | The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems |
| title_full_unstemmed | The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems |
| title_short | The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems |
| title_sort | stability and stabilization of infinite dimensional caputo time fractional differential linear systems |
| topic | fractional differential equations fractional diffusion systems caputo derivative stability and stabilization in hilbert spaces decomposition method |
| url | https://www.mdpi.com/2227-7390/8/3/353 |
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