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

2025/03/04 by Zeng-bao Wu, Tao Chen, Wu, Zeng-bao +9
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical methods in engineering #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2503.02669

openalex publication_date 2025/03/04 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Related

• Fractional partial differential variational inequality
• On nonlocal variational and quasi-variational inequalities with\n fractional gradient
• Stability for a stochastic fractional differential variational inequality with Lévy jump
• Fractional Elliptic Quasi-Variational Inequalities: Theory and Numerics
• Existence Theorems on Quasi-variational Inequalities over Banach Spaces and its Applications to Time-dependent Pure Exchange Economy