A new fractional differential quasi-variational inequality with Mittag-Leffler kernel in Hilbert spaces and its applications

Abstract: This paper considers a new fractional differential quasi-variational inequality with Mittag-Leffler kernel comprising a fractional differential equation with Mittag-Leffler kernel and a quasi-variational inequality in Hilbert spaces. Qualitative properties of the solution for the 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 system under mild conditions. Finally, the obtained abstract results are applied to analyze the unique solvability and stability for a multi-agent optimization problem and a price control problem.