  We study the translocation dynamics of a polymer chain threaded through a
nanopore by an external force. By means of diverse methods (scaling arguments,
fractional calculus and Monte Carlo simulation) we show that the relevant
dynamic variable, the translocated number of segments $s(t)$, displays an {\em
anomalous} diffusive behavior even in the {\em presence} of an external force.
The anomalous dynamics of the translocation process is governed by the same
universal exponent $\alpha = 2/(2\nu +2 - \gamma_1)$, where $\nu$ is the Flory
exponent and $\gamma_1$ - the surface exponent, which was established recently
for the case of non-driven polymer chain threading through a nanopore. A closed
analytic expression for the probability distribution function $W(s, t)$, which
follows from the relevant {\em fractional} Fokker - Planck equation, is derived
in terms of the polymer chain length $N$ and the applied drag force $f$. It is
found that the average translocation time scales as $\tau \propto
f^{-1}N^{\frac{2}{\alpha} -1}$. Also the corresponding time dependent
statistical moments, $< s(t) > \propto t^{\alpha}$ and $< s(t)^2 > \propto
t^{2\alpha}$ reveal unambiguously the anomalous nature of the translocation
dynamics and permit direct measurement of $\alpha$ in experiments. These
findings are tested and found to be in perfect agreement with extensive Monte
Carlo (MC) simulations.
