标题： Sibuya概率分布和分数阶算子的数值评估 显示英文标题

标题： Sibuya probability distributions and numerical evaluation of fractional-order operators

摘要： 本文研究了Sibuya离散概率分布，该分布作为数值模拟Grunwald–Letnikov分数阶导数的基础工具和主要手段，通过蒙特卡罗方法实现。我们提出了三种模拟Sibuya分布的方法。此外，我们引入了类似Sibuya的筛分概率分布，并将其应用于数值分数阶微分计算。同时，我们使用蒙特卡罗方法来评估分数阶积分，并提出了连续型Sibuya概率分布的概念。所开发的方法和工具通过计算实例进行了说明。我们提供了用于模拟Sibuya概率分布以及数值算例的MATLAB工具箱。 显示英文摘要

摘要： In this work we explore the Sibuya discrete probability distribution, which serves as the basis and the main instrument for numerical simulations of Grunwald--Letnikov fractional derivatives by the Monte Carlo method. We provide three methods for simulating the Sibuya distribution. We also introduce the Sibuya-like sieved probability distributions, and apply them to numerical fractional-order differentiation. Additionally, we use the Monte Carlo method for evaluating fractional-order integrals, and suggest the notion of the continuous Sibuya probability distribution. The developed methods and tools are illustrated by examples of computation. We provide the MATLAB toolboxes for simulation of the Sibuya probability distribution, and for the numerical examples.