The aim of this paper is to examine an evolution problem (FFDIVHVI) involving a fuzzy fractional differential inclusion and a variational–hemivariational inequality (VHVI) in Banach spaces. First, we show a uniqueness and existence theorem for VHVI under the theory of monotone operators and the surjectivity theorem. Then, by utilizing fixed point theorem for multivalued contraction mapping and fuzzy set theory, we establish the existence result for FFDIVHVI. In addition, it is proven that the collection of all mild trajectories of FFDIVHVI exhibits compactness. Finally, we illustrate the applicability of the abstract theory by a nonlinear quasistatic thermoelastic frictional contact problem for which we provide existence results.

中文翻译：

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Banach空间中变分半变分不等式驱动的模糊分数阶微分包含


本文的目的是研究涉及 Banach 空间中的模糊分数微分包含和变分半变分不等式 (VHVI) 的演化问题 (FFDIVHVI)。首先，我们在单调算子理论和满射定理下给出了VHVI的唯一性和存在性定理。然后，利用多值收缩映射的不动点定理和模糊集理论，建立了FFDIVHVI的存在性结果。此外，还证明了FFDIVHVI所有温和轨迹的集合表现出紧致性。最后，我们通过非线性准静态热弹性摩擦接触问题说明了抽象理论的适用性，并提供了存在结果。