  Fractional generalized Langevin equation with external force is used to model
single-file diffusion. It is found that for external force that varies with
power law the solution for such a fractional Langevin equation gives the
correct short and long time behavior for the mean square displacement of
single-file diffusion when appropriate choice of parameters associated with
fractional generalized Langevin equation are used. By considering some special
cases of the fractional generalized Langevin equation, a new class of closed
analytic expressions for the mean square displacement of single-file diffusion
can be obtained. The effective Fokker-Planck equation associated with
single-file diffusion is briefly considered.
