# Existence and controllability of fractional-order impulsive stochastic system with infinite delay

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

- Volume: 33, Issue: 1, page 65-87
- ISSN: 1509-9407

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topToufik Guendouzi. "Existence and controllability of fractional-order impulsive stochastic system with infinite delay." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.1 (2013): 65-87. <http://eudml.org/doc/270357>.

@article{ToufikGuendouzi2013,

abstract = {This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.},

author = {Toufik Guendouzi},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {existence result; approximate controllability; fractional stochastic differential equations; resolvent operators; infinite delay},

language = {eng},

number = {1},

pages = {65-87},

title = {Existence and controllability of fractional-order impulsive stochastic system with infinite delay},

url = {http://eudml.org/doc/270357},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Toufik Guendouzi

TI - Existence and controllability of fractional-order impulsive stochastic system with infinite delay

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2013

VL - 33

IS - 1

SP - 65

EP - 87

AB - This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.

LA - eng

KW - existence result; approximate controllability; fractional stochastic differential equations; resolvent operators; infinite delay

UR - http://eudml.org/doc/270357

ER -

## References

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