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In this paper, by comparing the time scales associated with the velocityrelaxation and correlation time of the random force due to dust chargefluctuations, memory effects in the velocity relaxation of an isolated dustparticle exposed to the random force due to dust charge fluctuations areconsidered, and the velocity relaxation process of the dust particle isconsidered as a non-Markovian stochastic process. Considering memory effects inthe velocity relaxation process of the dust particle yields a retarded frictionforce, which is introduced by a memory kernel in the fractional Langevinequation. The fluctuation-dissipation theorem for the dust grain is derivedfrom this equation. The mean-square displacement and the velocityautocorrelation function of the dust particle are obtained, and theirasymptotic behavior, the dust particle temperature due to charge fluctuations,and the diffusion coefficient are studied in the long-time limit. As aninteresting feature, it is found that by considering memory effects in thevelocity relaxation process of the dust particle, fluctuating force on the dustparticle can cause an anomalous diffusion in a dusty plasma. In this case, themean-square displacement of the dust grain increases slower than linearly withtime, and the velocity autocorrelation function decays as a power-law insteadof the exponential decay. Finally, in the Markov limit, these results are ingood agreement with those obtained from previous works for Markov (memoryless)process of the velocity relaxation.

Memory effects in the velocity relaxation process of the dust particle in dusty plasma