A New Nonlocal Fractional Differential Quasi-Variational Inequality in Hilbert Spaces with Applications

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 the 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.