A new nonlocal fractional differential quasi-variational inequality in Hilbert spaces with applications
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915407171944448 |
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| author | Wu, Zeng-bao Chen, Tao Zhang, Quan-guo Zeng, Yue Huang, Nan-jing Xiao, Yi-bin |
| author_facet | Wu, Zeng-bao Chen, Tao Zhang, Quan-guo Zeng, Yue Huang, Nan-jing Xiao, Yi-bin |
| contents | This paper considers a new nonlocal fractional differential quasi-variational inequality (NFDQVI) comprising a fractional differential equation with a nonlocal condition and a time-dependent quasi-variational inequality in Hilbert spaces. Qualitative properties of the solution for the time-dependent parameterized quasi-variational inequality are investigated, which improve some known results in the literature. Moreover, the unique existence of the solution and Hyers-Ulam stability are obtained for such a novel NFDQVI under mild conditions. Finally, the obtained abstract results for NFDQVI are applied to analyze the unique solvability and stability addressing a time-dependent multi-agent optimization problem and a time-dependent price control problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new nonlocal fractional differential quasi-variational inequality in Hilbert spaces with applications Wu, Zeng-bao Chen, Tao Zhang, Quan-guo Zeng, Yue Huang, Nan-jing Xiao, Yi-bin Optimization and Control This paper considers a new nonlocal fractional differential quasi-variational inequality (NFDQVI) comprising a fractional differential equation with a nonlocal condition and a time-dependent quasi-variational inequality in Hilbert spaces. Qualitative properties of the solution for the time-dependent parameterized quasi-variational inequality are investigated, which improve some known results in the literature. Moreover, the unique existence of the solution and Hyers-Ulam stability are obtained for such a novel NFDQVI under mild conditions. Finally, the obtained abstract results for NFDQVI are applied to analyze the unique solvability and stability addressing a time-dependent multi-agent optimization problem and a time-dependent price control problem. |
| title | A new nonlocal fractional differential quasi-variational inequality in Hilbert spaces with applications |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.02669 |