FRACTIONAL NONLINEAR DIFFUSION EQUATION: EXACT SOLUTIONS

This work is devoted to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Levy distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.