Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r< 2

M. Mohan Raja; V. Vijayakumar; Le Nhat Huynh; R. Udhayakumar; Kottakkaran Sooppy Nisar

doi:10.1186/s13662-021-03373-1

Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r< 2

M. Mohan Raja
, V. Vijayakumar
, Le Nhat Huynh
, R. Udhayakumar
, Kottakkaran Sooppy Nisar

Mathematics

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 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.

Original language	English
Article number	237
Journal	Advances in Difference Equations
Volume	2021
Issue number	1
DOIs	https://doi.org/10.1186/s13662-021-03373-1
State	Published - Dec 2021

Keywords

Approximate controllability
Fractional evolution inclusions
Generalized Clarke’s subdifferential
Hemivariational inequalities
Mainardi’s Wright-type function

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10.1186/s13662-021-03373-1

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title = "Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r< 2",

abstract = "In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 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.",

keywords = "Approximate controllability, Fractional evolution inclusions, Generalized Clarke{\textquoteright}s subdifferential, Hemivariational inequalities, Mainardi{\textquoteright}s Wright-type function",

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AU - Mohan Raja, M.

AU - Vijayakumar, V.

AU - Huynh, Le Nhat

AU - Udhayakumar, R.

AU - Nisar, Kottakkaran Sooppy

PY - 2021/12

Y1 - 2021/12

N2 - In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 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.

AB - In this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order 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.

KW - Approximate controllability

KW - Fractional evolution inclusions

KW - Generalized Clarke’s subdifferential

KW - Hemivariational inequalities

KW - Mainardi’s Wright-type function

UR - https://www.scopus.com/pages/publications/85104998677

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DO - 10.1186/s13662-021-03373-1

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SN - 1687-1839

VL - 2021

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 237

ER -

Results on the approximate controllability of fractional hemivariational inequalities of order 1 < r< 2

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Keywords

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