Generalized Langevin equation for solute dynamics in fluids with time-dependent friction

The generalized Langevin equation (GLE) for a Brownian particle (BP) in a bath under the influence of a moving external harmonic potential is derived. It is assumed that the friction coefficients of the bath particles depend on time. The found GLE has the usual form but its memory kernel is a generalization of the expression known as a Prony series used to approximate a number of memory functions from the literature. Analytical solutions are obtained for the mean and mean squared displacements assuming the overdamped character of motion of the BP.