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.
Categories: cond-mat.stat-mech