A lot of physical and chemical processes exhibit anomalous behavior in their transport and relaxation properties under the influence of an external field.To describe such anomalous diffusion process, several fractional Fokker-Planck equations (FFPE) have been introduced by replacing some integer order derivatives in the standard equations by their fractional analogues.Especially the time-independnet Smoluchowski-type FFPE, as a continuous limit of a continuous-time random walk with the Mittag-Leffier residence time distribution, has been proven to be powerful in describing the relaxation properties 1.