  We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional
derivatives $\frac{\partial}{\partial t}P(x,t)=D
\frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact
time-dependent solutions are found for $ \nu = \frac{2-\gamma}{1+ \gamma}$
($-\infty<\gamma \leq 2$). By considering the long-distance {\it asymptotic}
behavior of these solutions, a connection is established, namely
$q=\frac{\gamma+3}{\gamma+1}$ ($0<\gamma \le 2$), with the solutions optimizing
the nonextensive entropy characterized by index $q$ . Interestingly enough,
this relation coincides with the one already known for L\'evy-like
superdiffusion (i.e., $\nu=1$ and $0<\gamma \le 2$). Finally, for
$(\gamma,\nu)=(2, 0)$ we obtain $q=5/3$ which differs from the value $q=2$
corresponding to the $\gamma=2$ solutions available in the literature ($\nu<1$
porous medium equation), thus exhibiting nonuniform convergence.
