格点相空间上的分数阶Liouville方程
Fractional Liouville Equation on Lattice Phase-Space
摘要：
本文提出了相空间分数阶Liouville方程的格点模拟。提出了具有幂律长程跳跃相空间点阵的Liouville方程。我们证明了连续极限将该格点方程变换为具有关于连续相空间坐标的非整数阶共轭Riesz分数阶导数的Liouville方程。分数阶Liouville方程与这些Riesz分数阶导数的应用被认为是描述等离子体类非局部介质的性质。
英文摘要：
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.
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