论文标题
关于分数演算的基本特殊功能的教程
A Tutorial on the Basic Special Functions of Fractional Calculus
论文作者
论文摘要
在本教程调查中，我们回想起Mittag-Leffler和Wright类型的特殊功能的基本属性，这些功能在与分数计算有关的过程中相关。我们概述了这些功能的主要应用。对于Mittag-Leffler函数，我们分析了第二种的亚abel积分方程以及分数松弛和振荡现象。对于赖特的功能，我们将它们分两种区分。我们主要强调第二种在概率理论中的赖特函数的相关性与所谓的m-wright函数，该功能概括了高斯，并且与时间分数扩散方程相关。
In this tutorial survey we recall the basic properties of the special function of the Mittag-Leffler and Wright type that are known to be relevant in processes dealt with the fractional calculus. We outline the major applications of these functions. For the Mittag-Leffler functions we analyze the Abel integral equation of the second kind and the fractional relaxation and oscillation phenomena. For the Wright functions we distinguish them in two kinds. We mainly stress the relevance of the Wright functions of the second kind in probability theory with particular regard to the so-called M-Wright function that generalizes the Gaussian and is related with the time-fractional diffusion equation.
