Riemann-Liouville分数阶半线性发展型H-半变分不等式的可解性和最优控制  

SOLVABILITY AND OPTIMAL CONTROL FOR RIEMANN-LIOUVILLE FRACTIONAL SEMILINEAR EVOLUTION HEMIVARIATIONAL INEQUALITIES

作　　者：施翠云 SHI Cui-yun(School of Basic Science,Guilin University of Technology at Nanning,Nanning 530001,China)

机构地区：[1]桂林理工大学南宁分校基础学科部,广西南宁530001

出　　处：《数学杂志》2023年第4期307-322,共16页Journal of Mathematics

基　　金：广西自然科学基金基金资助(2021GXNSFAA220130,2022GXNSFAA035617)。

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.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.

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 

分 类 号：O231.4[理学—运筹学与控制论]