The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

We focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach...

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Main Authors: Dehao Ruan, Jiaowan Luo
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2018/7502514
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spelling doaj-e9a306d17ee5465e84e39f990a10c7072020-11-25T01:57:11ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/75025147502514The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian MotionDehao Ruan0Jiaowan Luo1Department of Probability and Statistics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, ChinaDepartment of Probability and Statistics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, ChinaWe focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach fixed point method. Moreover, an example is presented to illustrate our main results.http://dx.doi.org/10.1155/2018/7502514
collection DOAJ
language English
format Article
sources DOAJ
author Dehao Ruan
Jiaowan Luo
spellingShingle Dehao Ruan
Jiaowan Luo
The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
Discrete Dynamics in Nature and Society
author_facet Dehao Ruan
Jiaowan Luo
author_sort Dehao Ruan
title The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
title_short The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
title_full The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
title_fullStr The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
title_full_unstemmed The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion
title_sort existence, uniqueness, and controllability of neutral stochastic delay partial differential equations driven by standard brownian motion and fractional brownian motion
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2018-01-01
description We focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach fixed point method. Moreover, an example is presented to illustrate our main results.
url http://dx.doi.org/10.1155/2018/7502514
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AT jiaowanluo theexistenceuniquenessandcontrollabilityofneutralstochasticdelaypartialdifferentialequationsdrivenbystandardbrownianmotionandfractionalbrownianmotion
AT dehaoruan existenceuniquenessandcontrollabilityofneutralstochasticdelaypartialdifferentialequationsdrivenbystandardbrownianmotionandfractionalbrownianmotion
AT jiaowanluo existenceuniquenessandcontrollabilityofneutralstochasticdelaypartialdifferentialequationsdrivenbystandardbrownianmotionandfractionalbrownianmotion
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