论文标题
分数衍生物：傅立叶，大象，记忆效应，粘弹性材料和异常扩散
Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials and anomalous diffusions
论文作者
论文摘要
本文将出现在AMS的通知中，首先是简短的历史记录，该论文对分数演算的起点以及Leibniz和Fourier扮演的关键角色开始。傅立叶对分数衍生物的定义是通过使用称为半群的方法的现代技术引入和解开包装的。提出了分数衍生物理论的最新进展。此外，我们解决了科学界一些人提出的一些问题。最后，我们提出了三种不同的应用：人口增长，具有记忆，粘性材料和异常扩散。
This paper, that will appear in the Notices of the AMS, begins with a brief historical account of the beginnings of fractional calculus and the crucial roles played by Leibniz and Fourier. Fourier's definition of fractional derivative is introduced and unpacked by using the modern technique known as the method of semigroups. Recent advances on the theory of fractional derivatives are presented. Furthermore, we address some questions that have been raised by some in the scientific community. Finally, we present three different applications: population growth with memory, viscoleastic materials and anomalous diffusions.
