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arXiv · 2503.02669

A new nonlocal fractional differential quasi-variational inequality in Hilbert spaces with applications

Zeng-bao Wu·Tao Chen·Quan-guo Zhang·Yue Zeng·Nan-jing Huang·Yi-bin Xiao
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Abstract

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.

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Zeng-bao Wu, Tao Chen, Quan-guo Zhang, Yue Zeng, Nan-jing Huang, Yi-bin Xiao. 2025-03-04. A new nonlocal fractional differential quasi-variational inequality in Hilbert spaces with applications. https://arxiv.org/abs/2503.02669

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