An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators
In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed p...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2023-10-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/33429 |
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| author | Marimuthu Mohan Raja Velusamy Vijayakumar Juan J. Nieto Sumati Kumari Panda Anurag Shukla Kottakkaran Sooppy Nisar |
| author_facet | Marimuthu Mohan Raja Velusamy Vijayakumar Juan J. Nieto Sumati Kumari Panda Anurag Shukla Kottakkaran Sooppy Nisar |
| author_sort | Marimuthu Mohan Raja |
| collection | DOAJ |
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In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired.
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| format | Article |
| id | doaj-art-d5464a87cc1c49abad0a3d59448d8ea3 |
| institution | OA Journals |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-d5464a87cc1c49abad0a3d59448d8ea32025-08-20T02:04:00ZengVilnius University PressNonlinear Analysis1392-51132335-89632023-10-0128610.15388/namc.2023.28.33429An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operatorsMarimuthu Mohan Raja0Velusamy Vijayakumar1https://orcid.org/0000-0001-5976-5794Juan J. Nieto2https://orcid.org/0000-0001-8202-6578Sumati Kumari Panda3Anurag Shukla4Kottakkaran Sooppy Nisar5https://orcid.org/0000-0001-5769-4320Vellore Institute of TechnologyVellore Institute of TechnologyUniversity of Santiago de CompostelaGMR Institute of TechnologyRajkiya Engineering College KannaujPrince Sattam Bin Abdulaziz University In this paper, we investigate the effect of hemivariational inequalities on the approximate controllability of Caputo fractional differential systems. The main results of this study are tested by using multivalued maps, sectorial operators of type (P, η, r, γ ), fractional calculus, and the fixed point theorem. Initially, we introduce the idea of mild solution for fractional hemivariational inequalities. Next, the approximate controllability results of semilinear control problems were then established. Moreover, we will move on to the system involving nonlocal conditions. Finally, an example is provided in support of the main results we acquired. https://www.journals.vu.lt/nonlinear-analysis/article/view/33429hemivariational inequalitiesfractional derivativeapproximate controllabilitysectorial operatorsmild solutiongeneralized Clarke’s subdifferential |
| spellingShingle | Marimuthu Mohan Raja Velusamy Vijayakumar Juan J. Nieto Sumati Kumari Panda Anurag Shukla Kottakkaran Sooppy Nisar An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators Nonlinear Analysis hemivariational inequalities fractional derivative approximate controllability sectorial operators mild solution generalized Clarke’s subdifferential |
| title | An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators |
| title_full | An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators |
| title_fullStr | An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators |
| title_full_unstemmed | An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators |
| title_short | An analysis on the approximate controllability results for Caputo fractional hemivariational inequalities of order 1 < r < 2 using sectorial operators |
| title_sort | analysis on the approximate controllability results for caputo fractional hemivariational inequalities of order 1 r 2 using sectorial operators |
| topic | hemivariational inequalities fractional derivative approximate controllability sectorial operators mild solution generalized Clarke’s subdifferential |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/33429 |
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