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

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.