Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$
Abstract In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 1 < r < 2 $1< r<2$ . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, a...
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SpringerOpen
2021-05-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-021-03373-1 |
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doaj-e03f04d2f77f450e98f08c71a467b6a52021-05-09T11:40:41ZengSpringerOpenAdvances in Difference Equations1687-18472021-05-012021112510.1186/s13662-021-03373-1Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$M. Mohan Raja0V. Vijayakumar1Le Nhat Huynh2R. Udhayakumar3Kottakkaran Sooppy Nisar4Department of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyApplied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang UniversityDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityAbstract In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 1 < r < 2 $1< r<2$ . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.https://doi.org/10.1186/s13662-021-03373-1Approximate controllabilityHemivariational inequalitiesFractional evolution inclusionsMainardi’s Wright-type functionGeneralized Clarke’s subdifferential |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Mohan Raja V. Vijayakumar Le Nhat Huynh R. Udhayakumar Kottakkaran Sooppy Nisar |
| spellingShingle |
M. Mohan Raja V. Vijayakumar Le Nhat Huynh R. Udhayakumar Kottakkaran Sooppy Nisar Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ Advances in Difference Equations Approximate controllability Hemivariational inequalities Fractional evolution inclusions Mainardi’s Wright-type function Generalized Clarke’s subdifferential |
| author_facet |
M. Mohan Raja V. Vijayakumar Le Nhat Huynh R. Udhayakumar Kottakkaran Sooppy Nisar |
| author_sort |
M. Mohan Raja |
| title |
Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| title_short |
Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| title_full |
Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| title_fullStr |
Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| title_full_unstemmed |
Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| title_sort |
results on the approximate controllability of fractional hemivariational inequalities of order 1 < r < 2 $1< r<2$ |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2021-05-01 |
| description |
Abstract In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 1 < r < 2 $1< r<2$ . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results. |
| topic |
Approximate controllability Hemivariational inequalities Fractional evolution inclusions Mainardi’s Wright-type function Generalized Clarke’s subdifferential |
| url |
https://doi.org/10.1186/s13662-021-03373-1 |
| work_keys_str_mv |
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