  The non--static generalized Langevin equation and its corresponding
Fokker--Planck equation for the position of a viscous fluid particle were
solved in closed form for a time dependent external force. Its solution for a
constant external force was obtained analytically. The non--Markovian
stochastic differential equation, associated to the dynamics of the position
under a colored noise, was then applied to the description of the dynamics and
persistence time of particles constrained within absorbing barriers.
Comparisons with molecular dynamics were very satisfactory.
