Anomalous behaviors in fractional Fokker-Planck equation

We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are discussed analytically. The long-time asymptotic behavior of the second moment is determined by the scaling exponent imposed by the drift force fields. In the special case of the space scaling value nu = 1 and the time scaling value 7 = 1, our result can be classified according to the temporal scaling of the mean second moment of the tracer for large t: <<(x(2)(t))over bar>> proportional to t with xi = 1/4 for normal diffusion, and <<(x(2)(t))over bar>> proportional to t(eta) with eta > 1 and xi > 1/4 for superdiffusion.