A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

Chalishajar, Dimplekumar; Anguraj, A.; Malar, K.; Karthikeyan, K.

doi:10.3390/math4040060

Cited by 17 publications

(16 citation statements)

References 44 publications

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“…Generally speaking, there are two classes of impulsive equations. One is composed of instantaneous IDEs, for which the duration of the impulsive perturbation is very short compared to the entire evolution process, see for example, References [1,2]. The other class is composed of non-instantaneous IDEs, for which the impulsive action starts at a fixed point, and remains active over a period of time that may be related to the previous state.…”

Section: Introductionmentioning

confidence: 99%

“…The main objective of this article is to present the continuous dependence of solutions with respect to the initial condition when random impulse and junction points are incorporated in Equations (1) and (2). We will take notice of the fact that the location and the number of the impulse points and junction points are not determined in a finite time interval, and so, we can assume that the impulse and junction points are random.…”

Section: Introductionmentioning

confidence: 99%

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Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Wang

2019

Mathematics

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This paper gives continuous dependence results for solutions of integer and fractional order, non-instantaneous impulsive differential equations with random impulse and junction points. The notion of the continuous dependence of solutions of these equations on the initial point is introduced. We prove some sufficient conditions that ensure the solutions to perturbed problems have a continuous dependence. Finally, we use numerical examples to demonstrate the obtained theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Wang

2019

Mathematics

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“…The control problems involving the delay in state variable are challenging and are not much developed. Controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces is studied by Chalishajar et al [9]. Sikora and Klamka [28] studied the constrained controllability of fractional linear systems with delays in control.…”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlinear fractional Langevin delay systems

Kumar

Balachandran

Annapoorani

2019

NAMC

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In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α, β 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

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“…The theory of controllability of both linear and nonlinear SDEs have been broadly examined by numerous authors since it has various applications in science and technology. Controllability of SDEs with instantaneous impulses are studied recently in [5,12,20].…”

Section: Introductionmentioning

confidence: 99%

Second Order Stochastic Partial Integro Differential Equations with Delay and Impulses

Sastry

Deekshitulu

2019

cosa

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This paper manages the approximate controllability of second order neutral stochastic partial integro differential equations with infinite delay and non-instantaneous impulses. The results are acquired by employing Sadovskii's fixed point approach and firmly persistent cosine family of operators. A set of adequate stipulations for the approximate controllability of second order neutral stochastic partial integro differential equations with non-instantaneous impulses are provided beneath the situation that the relating linear system is approximately controllable. Further, an application is proposed to represent the acquired results.

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A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

Cited by 17 publications

References 44 publications

Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Controllability of nonlinear fractional Langevin delay systems

Second Order Stochastic Partial Integro Differential Equations with Delay and Impulses

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