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| 摘要: |
| 本文研究了Hilbert空间中半线性Riemann-Liouville分数阶发展型H-半变分不等式的可解性和最优控制.首先，利用不动点理论和Clarke广义次微分性质得到半线性Riemann-Liouville分数阶发展型H-半变分不等式解的存在性.其次，在一般假设条件下证明系统的最优控制存在性.最后，给出一个例子来验证本文的主要结果. |
| 关键词: 发展型H-半变分不等式 最优控制 Clarke广义次微分 Riemann-Liouville分数阶导数 |
| DOI： |
| 分类号:O231.4 |
| 基金项目:广西自然科学基金基金资助（2021GXNSFAA220130，2022GXNSFAA035617）. |
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| SOLVABILITY AND OPTIMAL CONTROL FOR RIEMANN-LIOUVILLE FRACTIONAL SEMILINEAR EVOLUTION HEMIVARIATIONAL INEQUALITIES |
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SHI Cui-yun
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| Abstract: |
| This paper studies the solvability and optimal control for fractional semilinear evolution hemivariational inequalities with Riemann-Liouville fractional derivative in Hilbert space. First, we prove the existence of mild solutions for this problem by using a fixed point theorem and some properties of generalized Clarke subdifferential. Next, under some generally suitable hypotheses, the existence result of the optimal control to the fractional evolution hemivariational inequalities with Riemann-Liouville fractional derivative is also presented and obtained. Finally, we give an example to illustrate our main results. |
| Key words: evolution hemivariational inequalities optimal control generalized clarke subdifferential Riemann-Liouville fractional derivative |
