论文标题
Prabhakar分数演算的实用指南
A practical guide to Prabhakar fractional calculus
论文作者
论文摘要
Mittag-Leffler函数普遍闻名为分数演算的女王功能。这项工作的目的是调查该功能的三参数概括（称为prabhakar函数）所产生的关键结果和应用。具体而言，在回顾了导致这种特殊功能的发现和现代发展的关键历史事件之后，我们讨论了后者如何允许人们引入分数计算的增强方案。然后，我们总结了该新的一般框架在物理和更新过程中的应用中的进度。我们还提供了有关Prabhakar函数的数值评估结果的集合。
The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the Prabhakar function. Specifically, after reviewing key historical events that led to the discovery and modern development of this peculiar function, we discuss how the latter allows one to introduce an enhanced scheme for fractional calculus. Then, we summarize the progress in the application of this new general framework to physics and renewal processes. We also provide a collection of results on the numerical evaluation of the Prabhakar function.
