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.