This paper is devoted to a generalized evolution system called fractional partial differential variational inequality which consists of a mixed quasi-variational inequality combined with a fractional partial differential equation in a Banach space. Invoking the pseudomonotonicity of multivalued operators and a generalization of the Knaster-Kuratowski-Mazurkiewicz theorem, first, we prove that the solution set of the mixed quasi-variational inequality involved in system is nonempty, closed and convex. Next, the measurability and upper semicontinuity for the mixed quasi-variational inequality with respect to the time variable and state variable are established. Finally, the existence of mild solutions for the system is delivered. The approach is based on the theory of operator semigroups, the Bohnenblust-Karlin fixed point principle for multivalued mappings, and theory of fractional operators.

中文翻译：

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一类由变分不等式和分数算子驱动的广义演化问题

本文致力于一个称为分数阶偏微分变分不等式的广义演化系统，该系统由混合准变分不等式和分数阶偏微分方程在Banach空间中组成。调用多值算子的伪单调性和Knaster-Kuratowski-Mazurkiewicz定理的推广，首先，我们证明系统中涉及的混合拟变分不等式的解集是非空的，封闭的和凸的。接下来，建立了关于时间变量和状态变量的混合准变分不等式的可测性和上半连续性。最后，系统存在温和解决方案。该方法基于算子半群理论，