Fractional Liouville Equation on Lattice Phase-Space
arXiv:1503.04351 · doi:10.1016/j.physa.2014.11.031
Abstract
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.
arXiv comment22 pages, LaTeX
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