  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 $\lambda$. We
obtain as well an exact expression for $\lambda$ for all kinds of diffusion.
Moreover, we show that $\lambda$ 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.
