An equation of long-range particle drift and diffusion on a 3D physical lattice is suggested. This equation can be considered as a lattice analog of the space-fractional Fokker-Planck equation for continuum. The lattice approach gives a possible microstructural basis for anomalous diffusion in media that are characterized by the non-locality of power law type. In continuum limit the suggested 3D lattice Fokker-Planck equations give fractional Fokker-Planck equations for continuous media with power law non-locality that is described by derivatives of non-integer orders. The consistent derivation of the fractional Fokker-Planck equation is proposed as a new basis to describe space-fractional diffusion processes.