Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (/) P (x, t) =D (^/x^) P (x, t) ^. Exact time-dependent solutions are found for = (2-) / (1+) (-<<~2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q= (+3) / (+1) (0<<~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. , =1 and 0<<~2). Finally, for (, ) = (2, 0) we obtain q=5/3, which differs from the value q=2 corresponding to the =2 solutions available in the literature (<1 porous medium equation), thus exhibiting nonuniform convergence.