  This is the second of a series of two papers which studies the fractional
porous medium equation, $\partial_t u +(-\Delta)^\sigma (|u|^{m-1}u )=0 $ with
$m>0$ and $\sigma\in (0,1]$, posed on a Riemannian manifold with isolated
conical singularities. The first aim of the article is to derive some useful
properties for the Mellin-Sobolev spaces including the Rellich-Kondrachov
Theorem and Sobolev-Poincar\'e, Nash and Super Poincar\'e type inequalities.
The second part of the article is devoted to the study the Markovian extensions
of the conical Laplacian operator and its fractional powers. Then based on the
obtained results, we establish existence and uniqueness of a global strong
solution for $L_\infty-$initial data and all $m>0$. We further investigate a
number of properties of the solutions, including comparison principle,
$L_p-$contraction and conservation of mass. Our approach is quite general and
thus is applicable to a variety of similar problems on manifolds with more
general singularities.
