  In this paper we propose a lattice analog of phase-space fractional Liouville
equation. The Liouville equation for phase-space lattice with long-range jumps
of power-law types is suggested. We prove that the continuum limit transforms
this lattice equation into Liouville equation with conjugate Riesz fractional
derivatives of non-integer orders with respect to coordinates of continuum
phase-space. An application of the fractional Liouville equation with these
Riesz fractional derivatives to describe properties of plasma-like nonlocal
media is considered.
