ABSTRACT In this paper, we mainly investigate controlled fractional evolution hemivariational inequalities of degenerate type in Caputo and Riemann–Liouville fractional derivatives of order in respectively. With the help of properties on fractional resolvent operators and generalised Clarke subdifferential, suitable concepts of solutions to addressed systems are formulated and existence results are established. And then, we present the existence of optimal state-control pairs for the limited Lagrange optimal systems governed by fractional evolution hemivariational inequalities of degenerate type. The optimal control results are attained by the compactness of some corresponding fractional resolvent operators.

中文翻译：

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退化型分数演化半变分不等式和通过分数解析算子的最优控制

摘要 在本文中，我们主要研究了分别在阶的 Caputo 和 Riemann-Liouville 分数阶导数中退化类型的受控分数演化半变分不等式。借助分数分解算子的性质和广义克拉克次微分，制定了解决系统的合适概念，并建立了存在性结果。然后，我们提出了由退化类型的分数演化半变分不等式支配的有限拉格朗日最优系统的最优状态-控制对的存在性。最优控制结果是通过一些相应的分数解析算子的紧凑性来获得的。