  We firstly prove Strichartz estimates for the fractional Schr\"odinger
equations on $\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then
prove Strichartz estimates for the fractional Schr\"odinger and wave equations
on compact Riemannian manifolds without boundary $(M,g)$. We finally give
applications of Strichartz estimates for the local well-posedness of the pure
power-type nonlinear fractional Schr\"odinger and wave equations posed on
$(M,g)$.
