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Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
We consider the nonlinear Fokker-Planck-like equation with fractional
derivatives . Exact
time-dependent solutions are found for
(). By considering the long-distance {\it asymptotic}
behavior of these solutions, a connection is established, namely
(), with the solutions optimizing
the nonextensive entropy characterized by index . Interestingly enough,
this relation coincides with the one already known for L\'evy-like
superdiffusion (i.e., and ). Finally, for
we obtain which differs from the value
corresponding to the solutions available in the literature (
porous medium equation), thus exhibiting nonuniform convergence.Comment: 3 figure