Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit

Michelitsch Thomas M.; Collet Bernard; Nowakowski Andrzej F.; Nicolleau Franck C. G. A.

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Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit

机译：有限周期线性链上的分数阶Laplacian矩阵及其周期Riesz分数阶导数连续极限

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We deduce explicit representations for the 1D discrete lattice counterpart of fractional Laplacian on the finite periodic linear chain. The continuum limit of the fractional lattice Laplacian operator yields the periodic Riesz fractional derivative on the finite periodic string. In the limiting case of infinite lattices known representations are recovered. The fractional finite-lattice Laplacian operator is of importance for the description and analysis of a wide range of problems of certain kinds of anomalous phenomena such as Levy flights and problems of fractional quantum mechanics.

机译：我们推导了有限周期线性链上分数拉普拉斯算子的一维离散晶格对应物的显式表示。分数格Laplacian算子的连续极限产生有限周期字符串上的周期Riesz分数导数。在无限格的极限情况下，恢复了已知的表示。分数有限格Laplacian算子对于描述和分析某些种类的异常现象（例如征费飞行）和分数量子力学问题的各种问题非常重要。

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来源
《Journal of physics, A. Mathematical and theoretical》 |2015年第29期|共27页
作者
Michelitsch Thomas M.; Collet Bernard; Nowakowski Andrzej F.; Nicolleau Franck C. G. A.;
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正文语种 eng
中图分类物理学;
关键词
finite domain fractional Laplacian-Riesz fractional derivative; power law matrix function; discrete fractional operators on periodic finite chains; fractional discrete approaches; fractional lattice models; continuum limit of fractional discrete models; Levy flights on finite lattices;

机译：有限域分数Laplacian-Riesz分数导数;幂律矩阵函数;周期有限链上的离散分数算子;分数离散方法;分数格模型;分数离散模型的连续极限;有限格上的征飞行;

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1. Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit [J] . Michelitsch Thomas M., Collet Bernard, Nowakowski Andrzej F., Journal of physics, A. Mathematical and theoretical . 2015,第29期

机译：有限周期线性链上的分数阶Laplacian矩阵及其周期Riesz分数阶导数连续极限
2. Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ -Riesz-Caputo Fractional Derivative [J] . Dandan Yang, Chuanzhi Bai Mathematics . 2019,第7期

机译：涉及ψ-Riesz-Caputo分数阶导数的反周期分数阶微分包含解的存在性
3. On Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order γ ∈ (0, 1] [J] . Kosticacute, Marko Journal of Mathematics and Statistics . 2017,第3期

机译：含γ∈（0，1]的Weyl-Liouville导数的抽象半线性分数包含的概周期解
4. LINEAR CHAIN OF COUPLED FRACTIONAL OSCILLATORS; RESPONSE DYNAMICS AND ITS CONTINUUM LIMIT [C] . B. N. Narahari Achar, Tanya Prozny, John W. Hanneken ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2007 . 2008

机译：耦合分数阶振荡器的线性链;响应动力学及其连续极限
5. Numerical Approximations for the Fractional Laplacian in Space-Fractional Reaction-Diffusion Equations [D] . ?Alzahrani, Saham 2020

机译：空间 - 分数反应扩散方程分数拉普拉斯的数值近似
6. Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving ψ-Caputo fractional derivative [O] . Bessem Samet, Hassen Aydi -1

机译：ψ-Caputo分数阶导数的反周期分数边值问题的Lyapunov型不等式
7. Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit : Discrete and continuous fractional Laplacian on finite periodic chain. [O] . Michelitsch, Thomas, Collet, Bernard, Nowakowski, Andrzej,, 2015

机译：有限周期线性链上的分数阶Laplacian矩阵及其周期Riesz分数阶导数连续谱极限：有限周期链上的离散和连续分数Laplacian矩阵。

Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit

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