APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION

In this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllabi...

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Main Author: Abbes Benchaabane
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2022-12-01
Series:Ural Mathematical Journal
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Online Access:https://umjuran.ru/index.php/umj/article/view/501
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author Abbes Benchaabane
author_facet Abbes Benchaabane
author_sort Abbes Benchaabane
collection DOAJ
description In this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.
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institution DOAJ
issn 2414-3952
language English
publishDate 2022-12-01
publisher Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
record_format Article
series Ural Mathematical Journal
spelling doaj-art-b1f9bf6b3d0748ef97196955de876e6a2025-08-20T02:54:42ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522022-12-018210.15826/umj.2022.2.005153APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTIONAbbes Benchaabane0Laboratory of Analysis and Control of Differential Equations ”ACED”, Univ. 8 May 1945 GuelmaIn this paper we consider a class of impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the approximate controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.https://umjuran.ru/index.php/umj/article/view/501approximate controllability, fixed point theorem, rosenblatt process, mild solution stochastic impulsive systems.
spellingShingle Abbes Benchaabane
APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
Ural Mathematical Journal
approximate controllability, fixed point theorem, rosenblatt process, mild solution stochastic impulsive systems.
title APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
title_full APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
title_fullStr APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
title_full_unstemmed APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
title_short APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION
title_sort approximate controllability of impulsive stochastic systems driven by rosenblatt process and brownian motion
topic approximate controllability, fixed point theorem, rosenblatt process, mild solution stochastic impulsive systems.
url https://umjuran.ru/index.php/umj/article/view/501
work_keys_str_mv AT abbesbenchaabane approximatecontrollabilityofimpulsivestochasticsystemsdrivenbyrosenblattprocessandbrownianmotion