Controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems

Sathya, R.; Balachandran, K.

doi:10.14232/ejqtde.2011.1.50

Cited by 8 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The controllability of system governed by impulsive stochastic partial differential systems and fractional impulsive stochastic partial differential systems has received more and more attention. For example, Sakthivel et al [36], Balachandran and Sathya [37], Arthi et al [38], and Ahmed [39] obtained the controllability of impulsive stochastic differential equations with fractional Brownian motion. The papers [27][28][29][30][31][32] studied the existence results for nonlinear impulsive differential and stochastic differential equations with not instantaneous impulse.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

Zhang

Jia

2018

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, we investigate a new class of fractional impulsive stochastic partial integro-differential equations with infinite delay in Hilbert spaces. By using the stochastic analysis theory, fractional calculus, analytic -resolvent operator and the fixed point technique combined with fractional powers of closed operators, we firstly give the existence of of mild solutions and optimal mild solutions for the these equations. Next, the controllability of the controlled fractional impulsive stochastic partial integro-differential systems with not instantaneous impulses is presented. Finally, examples are also given to illustrate our results. Key Words:Fractional impulsive stochastic partial integro-differential equations, optimal mild solutions, controllability, analytic -resolvent operators, fixed point. 1 p . Then ((H), ∥ ⋅ ∥  ) is a Banach space. Now, we give knowledge on the -resolvent operator which appeared in [4]. Definition 2.1. A one-parameter family of bounded linear operators ( (t)) t≥0 on H is called an -resolvent operator for c D t x(t) = Ax(t) + ∫ t 0 R(t − s)x(s)ds, x 0 = ∈ H, x ′ (0) = 0, (II.

show abstract

Section: Introductionmentioning

confidence: 99%

“…For example, Sakthivel et al. , Balachandran and Sathya , Arthi et al. , and Ahmed obtained the controllability of impulsive stochastic differential equations with fractional Brownian motion.…”

Section: Introductionmentioning

confidence: 99%

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

Zhang

Jia

2018

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…A standard approach is to transform the controllability problem into a fixed-point problem for an appropriate operator in a functional space. The problem of controllability for functional differential systems has been extensively studied in many papers [3,4,9,17,21,25]. For example, Sakthivel and Ren [24] studied the complete controllability of stochastic evolution equations with jumps.…”

Section: Introductionmentioning

confidence: 99%

Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Lakhel¹,

Tlidi²

2018

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert space. Sufficient conditions for controllability are obtained by employing a fixed point approach. A practical example is provided to illustrate the viability of the abstract result of this work.

show abstract

“…In [18], Mao studied the asymptotic properties of neutral stochastic differential delay equations. Sathya and Balachandran [23] proved sufficient conditions for controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems by means of the Banach fixed point theorem. By using the Sadovskii fixed point theorem, Muthukumar and Rajivganthi [19] investigated the approximate controllability of fractional order neutral stochastic integro-differential systems with nonlocal conditions and infinite delay.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Huan and Gao [11] have extended the results of the paper [10] for a class of nonlocal second-order impulsive neutral stochastic integro-differential equations with infnite delay and Poisson jumps. For more detail on the well-posedness and controllability of stochastic systems with impulsive effect, we refer the reader to [1,2,5,12,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory

Dang¹,

Agarwal

Gao

2017

Filomat

View full text Add to dashboard Cite

We establish results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert spaces. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Further, the above results are generalized to cover a class of much more general impulsive neutral stochastic delay partial differential equations driven by L?vy noise in infinite dimensions. Finally, an example is provided to illustrate our results.

show abstract

Controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems

Cited by 8 publications

References 25 publications

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory

Contact Info

Product

Resources

About