title: Analytical results for long-time behavior in anomalous diffusion.
abstract: 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.
authors.affiliation: Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-900 Fortaleza, Ceará, Brazil.
authors.forename: R M S
authors.initials: RM
authors.lastname: Ferreira
authors.forename: M V S
authors.initials: MV
authors.lastname: Santos
authors.forename: C C
authors.initials: CC
authors.lastname: Donato
authors.forename: J S
authors.initials: JS
authors.lastname: Andrade
authors.forename: F A
authors.initials: FA
authors.lastname: Oliveira