This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces. Under the suitable assumptions, the existence result is delivered by using the temporally semi-discrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, we propose a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The viscoelastic constitutive equation is modeled by fractional Kelvin-Voigt law with $\psi \text{-Caputo}$ derivative, and the frictional contact conditions are expressed as the Clarke subdifferentials of the nonconvex and nonsmooth functionals. Finally, the weak solvability of the mechanical system is obtained by using our abstract mathematical result.

本文研究了无限维空间中的广义分数半变分不等式。在适当的假设下，利用时间半离散格式和多值伪单调算子的满射性结果来传递存在性结果。作为一个说明性应用，我们提出了一种摩擦接触模型，该模型描述了粘弹性体和固体基础之间的准静态接触。粘弹性本构方程由分数 Kelvin-Voigt 定律建模$\psi \text{-卡普托}$导数，摩擦接触条件表示为非凸泛函和非光滑泛函的克拉克次微分。最后，利用我们抽象的数学结果，得到了机械系统的弱可解性。