  We consider and compare two different approaches to the fractional
subdiffusion and transport in washboard potentials. One is based on the concept
of random fractal time and is associated with the fractional Fokker-Planck
equation. Another approach is based on the fractional generalized Langevin
dynamics and is associated with anti-persistent fractional Brownian motion and
its generalizations. Profound differences between these two different
approaches sharing the common adjective "fractional" are explained in spite of
some similarities they share in the absence of a nonlinear force. In
particular, we show that the asymptotic dynamics in tilted washboard potentials
obey two different universality classes independently of the form of potential.
