A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional time differential operators instead of usual ones is also proposed to describe anomalous diffusion processes. Such equation can be regarded as corresponding to systems with incomplete Hamiltonian chaos, and, depending on the type of the relationship between the speed and coordinate of a particle, yields either usual or fractional long-time behavior of diffusion.into the equations of motion, either into the macroscopic Fokker-Planck equation (that leads to the fractional Fokker-Planck equation, 4) -8) ) or into the stochastic process defining microscopic motion of the particle. In the latter case a generalization of Wiener process called fractional Brownian motion was invented and gave way to by guest on March 22, 2015 http://ptps.oxfordjournals.org/ Downloaded from

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