Study of a generalized Langevin equation with nonlocal dissipative force,harmonic potential and a constant load force

We analyze the motion of a particle governed by a generalized Langevin equation with nonlocal dissipative force, linear external force and a constant load force. We consider the dissipative memory kernel consisting of two terms. One of them is described by the Dirac delta function which represents a local friction, whereas for the second one we consider two types: the exponential and power-law functions which represent nonlocal dissipative forces. For these cases, one can obtain exact results for the relaxation function. Then, we obtain the first moments and variances of the displacement and velocity. The long-time behaviors of these quantities are also investigated.