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We study the time behavior of the Fokker-Planck equation in Zwanzig rule (thebackward-Ito rule) based on the Langevin equation of Brownian motion with ananomalous diffusion in a complex medium. The diffusion coefficient is afunction in momentum space and follows a generalized fluctuation-dissipationrelation. We obtain the precise time-dependent analytical solution of theFokker-Planck equation and at long time the solution approaches to a stationarypower-law distribution in nonextensive statistics. As a test, numerically wehave demonstrated the accuracy and validity of the time-dependent solution.

The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion