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Start Over Author "Nisar, Kottakkaran Sooppy" Topic carleman theorem
6 results on '"Nisar, Kottakkaran Sooppy"'

1. Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities.

Author

Vijayakumar, V., Udhayakumar, R., Panda, Sumati Kumari, and Nisar, Kottakkaran Sooppy

Subjects
FRACTIONAL calculus, CARLEMAN theorem, EVOLUTION equations
Abstract

In our article, we primarily concentrate on the approximate controllability results for Sobolev type fractional stochastic evolution hemivariational inequalities. By applying the facts related to fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Existence and total controllability results of fuzzy delay differential equation with non-instantaneous impulses.

Author

Kumar, Anil, Malik, Muslim, and Nisar, Kottakkaran Sooppy

Subjects
IMPULSIVE differential equations, NONLINEAR functional analysis, DIFFERENTIAL equations, FUNCTIONAL differential equations, CARLEMAN theorem, DELAY differential equations, FUZZY numbers
Abstract

In this work, we consider a fuzzy delay differential system with non-instantaneous impulses and investigate the existence, uniqueness and total controllability results. Non-linear functional analysis, Banach fixed point theorem and fuzzy theory are the main techniques to establish these results. In support, an example is given to validate the obtained analytical outcomes. [ABSTRACT FROM AUTHOR]

Published
2021
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3. Results on the approximate controllability of fractional hemivariational inequalities of order 1<r<2.

Author

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

Subjects
LINEAR control systems, CARLEMAN theorem, CONTROLLABILITY in systems engineering, VARIATIONAL inequalities (Mathematics)
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. [ABSTRACT FROM AUTHOR]

Published
2021
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4. A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order [formula omitted].

Author

Shukla, Anurag, Vijayakumar, V., and Nisar, Kottakkaran Sooppy

Subjects
*SEMILINEAR elliptic equations, *CONTROLLABILITY in systems engineering, *GRONWALL inequalities, *CARLEMAN theorem, *FRACTIONAL calculus
Abstract

In this article, we mainly focus on the existence and approximate controllability results for the fractional semilinear impulsive control system of order r ∈ (1 , 2). We consider two different sets of sufficient conditions. In the first set, we derive the results by using the theories on the fractional calculus, compactness of the cosine family, and Schauder's fixed point theorem. In the second set, we prove the main results by using Gronwall's inequality, avoids the usage of the compactness of cosine family and fixed point theorems. By introducing the suitable assumptions, we discuss the existence and uniqueness of mild solutions for the fractional semilinear impulsive system. Finally, we provide theoretical and practical applications to assist in the effectiveness of the discussion. [ABSTRACT FROM AUTHOR]

Published
2022
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5. New discussion regarding approximate controllability for Sobolev-type fractional stochastic hemivariational inequalities of order [formula omitted].

Author

Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., Shukla, Anurag, and Nisar, Kottakkaran Sooppy

Subjects
*CONTROLLABILITY in systems engineering, *STOCHASTIC analysis, *STOCHASTIC systems, *SET-valued maps, *FRACTIONAL calculus, *CARLEMAN theorem
Abstract

In this paper, we deal with the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities of order r ∈ (1 , 2). Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, and fixed point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study. • Approximate controllability of fractional hemivariational inequalities are studied. • Stochastic theory, multimaps, and fixed point approach are used in the main results. • We begin by proving the existence of mild solutions of the considered system. • Next, approximate controllability of fractional stochastic control system are proved. • At last, some examples are provided to define the primary results. [ABSTRACT FROM AUTHOR]

Published
2023
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6. Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type.

Author

Kavitha, K., Vijayakumar, V., Shukla, Anurag, Nisar, Kottakkaran Sooppy, and Udhayakumar, R.

Subjects
*DIFFERENTIAL inclusions, *EVOLUTION equations, *SUBDIFFERENTIALS, *CARLEMAN theorem, *LINEAR systems, *MOTIVATION (Psychology), *FRACTIONAL calculus
Abstract

• The basic motivation of our article is the approximate controllability issues of delay evolution equations for Sobolev type with order 1

Published
2021
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