We obtain an exact form for the propagator of the Fokker-Planck equation ∂tρ = ∂x (D(x)∂x ρ) −∂x (F(x, t)ρ), with D(x) = D|x|−η in presence of the external force F(x, t) = −k(t)x + (K/x) |x|−η. Using the results found here, we also investigate the mean square displacement, survival probability, and first passage time distribution. In addition, we discuss the connection of these results with anomalous diffusion phenomena.


No Posts