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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn 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.

scholarly journals Approximate controllability of delayed semilinear control systems

2005 ◽  
Vol 2005 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Lianwen Wang
Keyword(s):  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Semilinear Control Systems

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations y˙(t)=Ay(t)+A1y(t−Δ)+F(t,y(t),yt)+(Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate controllability of a class of delayed semilinear control systems under natural assumptions.

scholarly journals A note on the approximate controllability of second-order integro-differential evolution control systems via resolvent operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Velusamy Vijayakumar ◽  
Anurag Shukla ◽  
Kottakkaran Sooppy Nisar ◽  
Wasim Jamshed ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Evolution ◽  
Control Systems ◽  
Approximate Controllability ◽  
Semigroup Theory ◽  
Second Order ◽  
Resolvent Operators ◽  
Gronwall’S Inequality ◽  
Evolution Control

AbstractThe approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and Lipschitz condition. The article avoids the use of well-known fixed point theorem approaches. We have also included one example of theoretical consequences that has been validated.

scholarly journals Controllability of nonlinear impulsive Ito type stochastic systems

2009 ◽  
Vol 19 (4) ◽  
pp. 589-595 ◽  
Author(s):  
Rathinasamy Sakthivel
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Complete Controllability ◽  
Natural Assumption ◽  
Fixed Point Approach ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Dynamical Control

Controllability of nonlinear impulsive Ito type stochastic systemsIn this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.

scholarly journals Solving an Integral Equation by Using Fixed Point Approach in Fuzzy Bipolar Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Absar Ul Haq ◽  
Fahd Jarad ◽  
Imran Abbas Baloch
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Uniqueness Of The Solution ◽  
Theoretical Results

The purpose of this manuscript is to obtain some fixed point results under mild contractive conditions in fuzzy bipolar metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation was studied as a kind of applications.

scholarly journals Existence of Second Order Impulsive Neutral Integro-Differential Evolution Control Systems with an Infinite Delay

2019 ◽  
Vol 8 (3) ◽  
pp. 8857-8862
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive neutral integrodifferential evolution systems with an infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals On the approximate controllability of semilinear control systems

2016 ◽  
Vol 3 (1) ◽  
pp. 1266773
Author(s):  
Divya Ahluwalia ◽  
N. Sukavanam ◽  
Anurag Shukla ◽  
Lishan Liu
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Semilinear Control Systems
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