Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lvy noise

This work is concerned with the existence of mild solutions to nonlinear Fokker-Planck equations with fractional Laplace operator ( - Delta ) s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(- \Delta )<^>s$$\end{document} for s is an element of 1 2 , 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s\in \left( \frac{1}{2},1\right) $$\end{document} . The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean-Vlasov equations with Levy noise, as well as the Markov property for their laws are proved.