This paper investigates a novel class of nonlinear dynamical fuzzy systems referred to as fuzzy fractional delay differential hemivariational inequalities (FFDDHVIs) in Banach spaces. These systems integrate fractional fuzzy differential inclusions with delay and hemivariational inequalities. The existence theorem for the HVIs is established based on the KKM theorem. Moreover, specific propositions are proved, covering the superpositional measurability and the upper semicontinuity for the HVIs. Next, by using the fixed points theorem, we establish the existence and compactness of mild solution sets for the FFDDHVIs under certain mild conditions. Finally, As an illustrative application, we investigate a frictional quasistatic contact problem for viscoelastic materials, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals.

中文翻译：

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Banach空间中半变分不等式驱动的模糊分数延迟微分包含

本文研究了巴拿赫空间中的一类新型非线性动态模糊系统，称为模糊分数延迟微分半变分不等式（FFDDHVI）。这些系统将分数模糊微分包含与延迟和半变分不等式相结合。 HVI 的存在定理是在 KKM 定理的基础上建立的。此外，还证明了具体的命题，包括 HVI 的叠加可测性和上半连续性。接下来，利用不动点定理，我们建立了 FFDDHVI 在某些温和条件下的温和解集的存在性和紧性。最后，作为一个说明性应用，我们研究了粘弹性材料的摩擦准静态接触问题，其中摩擦和接触条件由非凸和非光滑泛函的克拉克广义梯度来描述。