Approximate controllability and optimal controls of fractional evolution systems in abstract spaces
© 2014, Qin et al.; licensee Springer.In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by...
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| Format: | Journal Article |
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SpringerOpen
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/62500 |
| _version_ | 1848760863192776704 |
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| author | Qin, H. Liu, J. Zuo, X. Liu, Lishan |
| author_facet | Qin, H. Liu, J. Zuo, X. Liu, Lishan |
| author_sort | Qin, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2014, Qin et al.; licensee Springer.In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by means of the Hölder inequality, the Banach contraction mapping principle, and the Schauder fixed point theorem. We also discuss the existence of optimal controls for semilinear fractional controlled systems. Finally, an example is also given to illustrate the applications of the main results. MSC:26A33, 49J15, 49K27, 93B05, 93C25. |
| first_indexed | 2025-11-14T10:22:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-62500 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:22:32Z |
| publishDate | 2014 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-625002018-02-01T05:58:10Z Approximate controllability and optimal controls of fractional evolution systems in abstract spaces Qin, H. Liu, J. Zuo, X. Liu, Lishan © 2014, Qin et al.; licensee Springer.In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by means of the Hölder inequality, the Banach contraction mapping principle, and the Schauder fixed point theorem. We also discuss the existence of optimal controls for semilinear fractional controlled systems. Finally, an example is also given to illustrate the applications of the main results. MSC:26A33, 49J15, 49K27, 93B05, 93C25. 2014 Journal Article http://hdl.handle.net/20.500.11937/62500 10.1186/1687-1847-2014-322 SpringerOpen unknown |
| spellingShingle | Qin, H. Liu, J. Zuo, X. Liu, Lishan Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title | Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title_full | Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title_fullStr | Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title_full_unstemmed | Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title_short | Approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| title_sort | approximate controllability and optimal controls of fractional evolution systems in abstract spaces |
| url | http://hdl.handle.net/20.500.11937/62500 |