Controllability of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay

Li, Yong; Zou, Qiang

doi:10.1155/2013/419156

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…The concept of controllability, when it was first introduced by Kalman [13] in 1963, plays an important part in the analysis and design of control systems, and more details can be found in papers [1,3,6,8,18]. Some authors [4, 5, 9] have studied the exact controllability for nonlinear evolution systems by using fixed point theorems.…”

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confidence: 99%

Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces

Liu¹,

Bin²

2014

J. Integral Equations Applications

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In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce P C 1−α -mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.

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confidence: 99%

Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces

Liu¹,

Bin²

2014

J. Integral Equations Applications

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“…Sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multivalued operators due to Dhage [15]. Li and Zou [23] obtained sufficient conditions for the controllability of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert space with using a fixed-point theorem for condensing maps due to ORegan [29]. Li and Peng [24], Ganesh Priya and Muthukumar [31] studied the controllability of a class of fractional stochastic functional differential systems.…”

Section: Remark 42mentioning

confidence: 99%

“…Li and Peng [24], Ganesh Priya and Muthukumar [31] studied the controllability of a class of fractional stochastic functional differential systems. Based on these works, the exact controllability of the system 2.1 can be done by relying on a fixed-point theorem for condensing maps due to ORegan [29] and employing the idea and technique as in Theorem 8 in [23].…”

Section: Remark 42mentioning

confidence: 99%

Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay

Slama

Boudaoui

2017

Arab. J. Math.

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In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust-Karlin's fixed point theorem, a new set of sufficient conditions are formulated and proved for the existence of solutions and the approximate controllability of fractional nonlinear stochastic differential inclusions under the assumption that the associated linear part of the system is approximately controllable. An example is provided to illustrate the theory. Mathematics Subject Classification

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Approximate controllability for a new class of stochastic functional differential inclusions with infinite delay

Kumar

Yadav

2022

Random Operators and Stochastic Equations

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This manuscript investigates the approximate controllability for a wide range of infinite-delayed semilinear stochastic differential inclusions. First, we construct the expression for a mild solution in terms of the fundamental solution. Then, employing the fixed point theorem for multivalued maps, we formulate a set of sufficient conditions to assure the existence of a solution for the aforementioned system. Further, the approximate controllability for the semilinear stochastic differential inclusion is investigated under the condition that the associated linear deterministic control system is approximately controllable. The discussed results are more general and a continuation of the ongoing research on this issue. Finally, an example is included to highlight the applicability of the considered results.

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Controllability of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay

Abstract: The paper is concerned with the controllability of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert space. Sufficient conditions for the controllability are obtained by using a fixed-point theorem for condensing maps due to O'Regan.

Cited by 3 publications

References 25 publications

Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces

Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces

Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay

Approximate controllability for a new class of stochastic functional differential inclusions with infinite delay

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