Explicit Barenblatt Profiles for Fractional Porous Medium Equations

Several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators. The corresponding self-similar profiles, also called \emph{Barenblatt profiles}, have the same forms as those of the classic porous medium equations. These new exact solutions complement current theoretical analysis of the underlying equations and are expected to provide insights for further quantitative investigations.