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We study the generalized Langevin equation approach to anomalous diffusionfor a harmonic oscillator and a free particle driven by different forms ofinternal noises, such as power-law-correlated and distributed-order noises thatfulfil generalized versions of the fluctuation-dissipation theorem. The meansquared displacement and the normalized displacement correlation function arederived for the different forms of the friction memory kernel. Thecorresponding overdamped generalized Langevin equations for these cases arealso investigated. It is shown that such models can be used to describeanomalous diffusion in complex media, giving rise to subdiffusion,superdiffusion, ultraslow diffusion, strong anomaly, and other complexdiffusive behaviors.

Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises