Analytical results for long time behavior in anomalous diffusion

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor $λ$. We obtain as well an exact expression for $λ$ for all kinds of diffusion. Moreover, we show that $λ$ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem.

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