Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises
In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild solutions. In particular, approximate strategy is use...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/2/30 |
| _version_ | 1797538021972639744 |
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| author | Lixu Yan Yongqiang Fu |
| author_facet | Lixu Yan Yongqiang Fu |
| author_sort | Lixu Yan |
| collection | DOAJ |
| description | In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild solutions. In particular, approximate strategy is used to obtain the existence of mild solutions for the problem with linear fractional noises; fixed point theorem is used to achieve the existence of mild solutions for the problem with nonlinear fractional noises. Finally, the approximate controllability of the problems with linear and nonlinear fractional noises is proved by the property of mild solutions. |
| first_indexed | 2024-03-10T12:24:33Z |
| format | Article |
| id | doaj.art-dea368e841004df4aef413f47b289ebc |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T12:24:33Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-dea368e841004df4aef413f47b289ebc2023-11-21T15:13:39ZengMDPI AGFractal and Fractional2504-31102021-04-01523010.3390/fractalfract5020030Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid NoisesLixu Yan0Yongqiang Fu1School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaIn this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild solutions. In particular, approximate strategy is used to obtain the existence of mild solutions for the problem with linear fractional noises; fixed point theorem is used to achieve the existence of mild solutions for the problem with nonlinear fractional noises. Finally, the approximate controllability of the problems with linear and nonlinear fractional noises is proved by the property of mild solutions.https://www.mdpi.com/2504-3110/5/2/30fully nonlocal derivative operatormild solutionapproximate controllabilityfractional Brownian motionPoisson jump |
| spellingShingle | Lixu Yan Yongqiang Fu Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises Fractal and Fractional fully nonlocal derivative operator mild solution approximate controllability fractional Brownian motion Poisson jump |
| title | Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises |
| title_full | Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises |
| title_fullStr | Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises |
| title_full_unstemmed | Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises |
| title_short | Approximate Controllability of Fully Nonlocal Stochastic Delay Control Problems Driven by Hybrid Noises |
| title_sort | approximate controllability of fully nonlocal stochastic delay control problems driven by hybrid noises |
| topic | fully nonlocal derivative operator mild solution approximate controllability fractional Brownian motion Poisson jump |
| url | https://www.mdpi.com/2504-3110/5/2/30 |
| work_keys_str_mv | AT lixuyan approximatecontrollabilityoffullynonlocalstochasticdelaycontrolproblemsdrivenbyhybridnoises AT yongqiangfu approximatecontrollabilityoffullynonlocalstochasticdelaycontrolproblemsdrivenbyhybridnoises |