  The reactive process of barrier escaping from the metastable potential well
is studied together with the extension of Kramers' rate formula to the
fractional case. Characteristic quantities are computed for an thimbleful of
insight into the near barrier escaping and recrossing dynamics. Where the
stationary transmission coefficient is revealed to be larger than the usual
cases which implies less barrier recrossing. And the non-monotonic varying of
it reveals a close dependence to the fractional exponent $\alpha$. In most
cases, the near barrier behavior of the escaping dynamics is equivalent to the
diffusion in the two-dimensional non-Ohmic damping system.
