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...
Saved in:
| Main Author: | |
|---|---|
| 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 |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/501 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850045448483504128 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-b1f9bf6b3d0748ef97196955de876e6a |
| 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 |