论文标题
在两类的广义分数操作员（对分数演算的历史调查简短）上
On two classes of generalized fractional operators (with short historical survey of fractional calculus)
论文作者
论文摘要
这是两部分的调查文件。在第一部分中，我们列出了一维分数集成差异运算符的主要变体。还提供了一些历史和优先级的评论。作为一个特殊的问题，我们考虑了苏联和俄罗斯研究对分数演算的影响及其对粘弹性理论的应用。我们还强调了Voronezh力学和粘弹性理论的影响，包括Shermergor，Meschkov，Rossikhin，Shitikova等作品。在本文的第二部分中，我们考虑了两种重要的特殊类别的特殊类别分数操作员，作者对他们进行了彻底的研究。我们考虑Buschman-Erdelyi运营商，这是一个重要的类，其中包含特殊案例Riemann-Liouville，Erdélyi-Kober，Mehler-Fock运营商等。它们还包括用于贝塞尔差异操作员的古典传播，即Sonine和Poisson。之后，我们代表了Riemann-Liouville运营商的另一个重要概括，即Bessel运营商的分数力量。该论文专门针对亚当·马里莫维奇·纳库什夫（Adam Maremovich Nakhushev） - 出色的人和数学家。
This is a survey paper in two parts. In the first part we list main variants of one-dimensional fractional integrodifferential operators. Also some historical and priority remarks are given. As a special question we consider the impact of Soviet and Russian researches to fractional calculus and its applications to viscoelasticity theory. We also stress an impact of the Voronezh school of mechanics and viscoelasticity theory, including works of Shermergor, Meschkov, Rossikhin, Shitikova and others. In the second part of the paper we consider two important special classes of generalized fractional operators, they were thoroughly studied by the authors. We consider Buschman-Erdelyi operators, this is an important class containing as special cases Riemann-Liouville, Erdélyi-Kober, Mehler-Fock operators and some others. They also include classical transmutations for the Bessel differential operator, namely Sonine and Poisson ones. After that we represent results on another important generalization of Riemann-Liouville operators, namely fractional powers of the Bessel operators. The paper is dedicated to Adam Maremovich Nakhushev -- brilliant man and mathematician.
