Approximate controllability of fractional stochastic evolution equations

Sakthivel, R.; Suganya, S.; Anthoni, S. Marshal

doi:10.1016/j.camwa.2011.11.024

Cited by 156 publications

(93 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The biggest difficulty is the analysis of a stochastic control system and stochastic calculations induced by the stochastic process. For more details, see [14,16,19,23,34,36,39,50,52].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Chadha¹,

Bora²,

Sakthivel³

2018

DSA

Self Cite

View full text Add to dashboard Cite

This paper studies the approximate controllability of an impulsive neutral stochastic integro-differential equation with nonlocal conditions and infinite delay involving the Caputo fractional derivative of order q ∈ (1, 2) in separable Hilbert space. The existence of the mild solution to fractional stochastic system with nonlocal and impulsive conditions is first proved utilizing fixed point theorem, stochastic analysis, fractional calculus and solution operator theory. Then, a new set of sufficient conditions proving approximate controllability of nonlocal semilinear fractional stochastic system involving impulsive effects is derived by assuming the associated linear system is approximately controllable. Illustrating the obtained abstract results, an example is considered at the end of the paper.

show abstract

“…The biggest difficulty is the analysis of a stochastic control system and stochastic calculations induced by the stochastic process. For more details, see [14,16,19,23,34,36,39,50,52].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Chadha¹,

Bora²,

Sakthivel³

2018

DSA

Self Cite

View full text Add to dashboard Cite

show abstract

“…The problem of controllability of nonlinear stochastic or deterministic system has been discussed in [3,4,6,8,9,16,19].…”

Section: Introductionmentioning

confidence: 99%

Null controllability of nonlocal Hilfer fractional stochastic differential equations

JinRong¹,

Ahmed²

2017

MMN

View full text Add to dashboard Cite

Abstract. In this paper, we study exact null controllability of Hilfer fractional semilinear stochastic differential equations in Hilbert spaces. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional systems are established. An example is given to show the application of our results.2010 Mathematics Subject Classification: 26A33; 93B05

show abstract

“…In contrast, papers dealing with the approximate controllability of fractional order stochastic systems are scarce. Recently, the subject was addressed in Sakthivel et al [23] without Poisson jumps.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we move from deterministic impulsive fractional differential equations to stochastic impulsive fractional differential equations with Poisson jumps for the study of existence of solutions and controllability properties. Motivated by few studies [7], [18], [23], [22], the existence of solutions and approximate controllability of the following impulsive fractional stochastic differential system with infinite delay and Poisson jumps remains an untreated topic in the literature:…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps

et al. 2015

View full text Add to dashboard Cite

Approximate controllability of fractional stochastic evolution equations

Cited by 156 publications

References 24 publications

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

Null controllability of nonlocal Hilfer fractional stochastic differential equations

Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps

Contact Info

Product

Resources

About