In this paper, a two-parameter extension of the operational calculus of Mikusiński's type for the Caputo fractional derivative is presented. The first parameter is connected with the rings of functions that are used as a basis for construction of the convolution quotients fields. The convolutions by themselves are characterized by another parameter. The obtained two-parameter operational calculi are compared each to other and some homomorphisms between the fields of convolution quotients are established.

中文翻译：

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关于 Caputo 分数阶导数的 Mikusiński 型运算演算的扩展

在本文中，提出了用于 Caputo 分数阶导数的 Mikusiński 类型的运算微积分的双参数扩展。第一个参数与函数环相连，这些函数环用作构造卷积商域的基础。卷积本身由另一个参数表征。将得到的两参数运算演算相互比较，并建立卷积商域之间的一些同态。