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 d erivatives (partial derivative/partial derivative t)P(x,t) =D(partial deriv ative(gamma)/partial derivative x(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2- gamma)/(1 + gamma)(-infinity< y less than o r equal to 2). By considering the long-distance asymptotic behavior of thes e solutions, a connection is established, namely, q =(gamma+ 3)/(y + 1)(0<g amma less than or equal to 2), with the solutions optimizing the nonextensi ve entropy characterized by index q. Interestingly enough, this relation co incides with the one already known for Levy-like superdiffusion (i.e., nu = 1 and 0<gamma less than or equal to 2). Finally, for (gamma,nu)=(2,0) we o btain 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 e xhibiting nonuniform convergence.