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: Marimuthu Mohan Raja, Velusamy Vijayakumar, Juan J. Nieto, Sumati Kumari Panda, Anurag Shukla, Kottakkaran Sooppy Nisar
Format: Article
Language:English
Published: Vilnius University Press 2023-10-01
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
description 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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issn 1392-5113
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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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