Summary: We analyze the motion of a particle governed by a generalized Langevin equation with the colored noise described by a combination of power-law and generalized Mittag-Leffler function. This colored noise generalizes the power-law correlation function and an exponential one. We obtain exact results for the relaxation function. Further, we obtain the first moments and variances of the displacement and velocity. The long-time behavior of these quantities are also investigated. We show that normal diffusion processes can be generated by a class of these colored noises.{
©2009 American Institute of Physics}