The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability
In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equival...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/6179980 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559507981467648 |
|---|---|
| author | Li Chen-Yu |
| author_facet | Li Chen-Yu |
| author_sort | Li Chen-Yu |
| collection | DOAJ |
| description | In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form. |
| format | Article |
| id | doaj-art-b33c261aa18d4d14a1423db65e883840 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b33c261aa18d4d14a1423db65e8838402025-02-03T01:29:50ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/6179980The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its ObservabilityLi Chen-Yu0College of Computer ScienceIn this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form.http://dx.doi.org/10.1155/2024/6179980 |
| spellingShingle | Li Chen-Yu The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability Journal of Mathematics |
| title | The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability |
| title_full | The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability |
| title_fullStr | The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability |
| title_full_unstemmed | The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability |
| title_short | The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability |
| title_sort | hautus type inequality for abstract fractional cauchy problems and its observability |
| url | http://dx.doi.org/10.1155/2024/6179980 |
| work_keys_str_mv | AT lichenyu thehautustypeinequalityforabstractfractionalcauchyproblemsanditsobservability AT lichenyu hautustypeinequalityforabstractfractionalcauchyproblemsanditsobservability |