Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls
In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2019-02-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/12896 |
| _version_ | 1818365262811889664 |
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| author | Yatian Pei Yong-Kui Chang |
| author_facet | Yatian Pei Yong-Kui Chang |
| author_sort | Yatian Pei |
| collection | DOAJ |
| description | In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system. |
| first_indexed | 2024-12-13T22:17:28Z |
| format | Article |
| id | doaj.art-b3c31b5147b648e690ee6a38ceb0e210 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-13T22:17:28Z |
| publishDate | 2019-02-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-b3c31b5147b648e690ee6a38ceb0e2102022-12-21T23:29:28ZengVilnius University PressNonlinear Analysis1392-51132335-89632019-02-0124210.15388/NA.2019.2.3Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controlsYatian Pei0Yong-Kui Chang1Xidian UniversityXidian UniversityIn this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. We first establish sufficient conditions for the existence of mild solutions to the addressed control system via properties of generalized Clarke subdifferential and a fixed point theorem for condensing multivalued maps. Then we present the existence of optimal state-control pairs of the limited Lagrange optimal systems governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition. The optimal control results are derived without uniqueness of solutions for the control system.http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/12896Hilfer fractional evolution equationoptimal state-control pairshemivariational inequalitiesnonlocal initial condition |
| spellingShingle | Yatian Pei Yong-Kui Chang Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls Nonlinear Analysis Hilfer fractional evolution equation optimal state-control pairs hemivariational inequalities nonlocal initial condition |
| title | Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| title_full | Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| title_fullStr | Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| title_full_unstemmed | Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| title_short | Hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| title_sort | hilfer fractional evolution hemivariational inequalities with nonlocal initial conditions and optimal controls |
| topic | Hilfer fractional evolution equation optimal state-control pairs hemivariational inequalities nonlocal initial condition |
| url | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/12896 |
| work_keys_str_mv | AT yatianpei hilferfractionalevolutionhemivariationalinequalitieswithnonlocalinitialconditionsandoptimalcontrols AT yongkuichang hilferfractionalevolutionhemivariationalinequalitieswithnonlocalinitialconditionsandoptimalcontrols |