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This paper investigates the motion of a Brownian particle experiencing both a friction (biased) force and a randomly fluctuating force with a long-time-correlation function C₅ (t) t^-, 01, 12, and =1, instead of a Dirac function. The generalized Langevin equation and Fokker-Planck equation and corresponding solution are presented. It is shown that when 01 or 12, the diffusion motion of the Brownian particle is the anomalous diffusion that is related to fractal Brownian motion (FBM). But when =1 the diffusion motion is anomalous diffusion with no connection to FBM. The effects of friction retardation result in a probability density function for finding the particle at displacement X at time t that depends on the initial value of velocity of the particle. The approach in this paper may provide a systematic method for the study of particles diffusing in fractal media.
K. G. Wang (Wed,) studied this question.