Approximate controllability of non-autonomous Sobolev type integro-differential equations having nonlocal and non-instantaneous impulsive conditions

Meraj, Arshi; Pandey, Dwijendra N.

doi:10.1007/s13226-020-0413-9

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Secondly, we will explore the optimal control for non-instantaneous ISEEs excited by fBm with Hurst parameter H ∈ (0, 1/2). Thirdly, based on our method and recent studies on the controllability of deterministic non-instantaneous impulsive differential equations with non-local conditions [39,40], we will investigate the approximate controllability of non-instantaneous impulsive stochastic differential systems driven by fBm with non-local conditions in detail.…”

Section: Discussionmentioning

confidence: 99%

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

Liu

Wei

2022

Fractal Fract

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This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index 0<H<1122. First, to overcome the irregular or singular properties of fBm with Hurst parameter 0<H<1122, we define a new type of control function. Then, by virtue of the stochastic analysis theory, inequality technique, the semigroup approach, Krasnoselskii’s fixed-point theorem and Schaefer’s fixed-point theorem, we derive two new sets of sufficient conditions for the existence and approximate controllability of the concerned system. In the end, a concrete example is worked out to demonstrate the applicability of our obtained results.

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Section: Discussionmentioning

confidence: 99%

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

Liu

Wei

2022

Fractal Fract

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“…Recently, the researchers derived results on exact and approximate controllability for several systems like neutral systems, integrodifferential equations, impulsive systems, fixed delay systems, time‐varying delay systems, etc. Previously, many researcher's 1–28 studied exact and approximate controllability for the different type of systems.…”

Section: Introductionmentioning

confidence: 99%

“…They also present results in 1D space as a sufficient condition of Kalman's criteria. Under Lion boundary conditions, the 3D Navier–Stokes system is approximately controllable discussed by Phan et al 6 Meraj and Pandey 13 derived the outcomes about approximate controllability for a nonautonomous system having nonlocal initial condition using Krasnoselski theorem and evolution system.…”

Section: Introductionmentioning

confidence: 99%

A discussion on boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations

Kumar¹,

Patel²,

Vijayakumar

et al. 2022

Math Methods in App Sciences

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Sufficient conditions for boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations are explored. In the first problem, the outcomes are proven with the help of Sadovskii's fixed point theorem collaborated with strongly continuous semigroup theory. In the second problem, we considered nonautonomous evolution equations, and the result is proven by employing Sadovskii's fixed point theorem in collaboration with the evolution system. Examples are included to demonstrate the theoretical results for both types of equations.

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“…In such a way, the approximate controllability is completely adequate in applications. For readers, we refer to some interesting and important controllability results 5,[12][13][14][15][16][17][18][19][20] concerning semilinear or nonlinear differential systems in which semigroup theory and some fixed-point theorems are used. In Jeet and Sukavanam 12 and Wang et al, 21 the authors studied the approximate controllability of nonlocal and impulsive semilinear system using an approximating technique.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of nonlocal impulsive neutral integro‐differential equations with finite delay

Jeet

Pandey

2021

Math Methods in App Sciences

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In this paper, we apply the resolvent operator theory and an approximating technique to derive the existence and controllability results for nonlocal impulsive neutral integro-differential equations with finite delay in a Hilbert space. To establish the results, we take the impulsive functions as a continuous function only, and we assume that the nonlocal initial condition is Lipschitz continuous function in the first case and continuous functions only in the second case. The main tools applied in our analysis are semigroup theory, the resolvent operator theory, an approximating technique, and fixed-point theorems. Finally, we illustrate the main results with the help of two examples.

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Approximate controllability of non-autonomous Sobolev type integro-differential equations having nonlocal and non-instantaneous impulsive conditions

Cited by 8 publications

References 16 publications

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

A discussion on boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations

Approximate controllability of nonlocal impulsive neutral integro‐differential equations with finite delay

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