Sensitivity analysis for optimal control problems governed by Hilfer fractional differential hemivariational inequalities

This paper studies a sensitivity analysis of optimal control problems for a new class of systems described by Hilfer fractional differential hemivariational inequalities (HFDHVIs) on Hilbert spaces, where the initial state ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} is not the Cauchy boundary condition, but is the Riemann–Liouville integral boundary condition. First, we obtain the nonemptiness as well as the compactness property of the mild solution set S(ξ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {S}(\xi )$$\end{document} for HFDHVIs, and also establish an infinite dimensional version of Filippov’s theorem whose proof differs from previous work only in some technical details. Then we obtain the sensitivity analysis of optimal control problems associated with HFDHVIs depending on the initial state ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} and the parameter λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}. Finally, an illustrating example is given.