关于分数阶算子的若干几何解释
历史与综述
2024-11-20 v1
摘要
本文讨论了正在进行的工作的部分内容。文中指出，G.W. Leibniz 是最早提出分数阶算子几何解释问题的人。解释了 Riemann--Liouville 分数阶积分与 Stieltjes 积分的几何解释。随后，首次引入了 Stieltjes 导数的几何解释，该解释同样适用于所谓的“分形导数”，后者是 Stieltjes 导数的一种特殊情形。
引用
@article{arxiv.2411.12494,
title = {On some geometric interpretations of fractional-order operators},
author = {Igor Podlubny},
journal= {arXiv preprint arXiv:2411.12494},
year = {2024}
}
备注
3 pages, 4 figures. This work has been submitted as discussion paper 074 and presented as talk WeB02.2 (Wednesday, July 9, 2024, 16:40-17:00) at \textit {ICFDA'2024 -- 12th IFAC Conference on Fractional Differentiation and its Applications, Bordeaux, France, July 9--12, 2024.}