论文标题
第一级一般分数衍生物及其某些特性
The 1st Level General Fractional Derivatives and some of their Properties
论文作者
论文摘要
在本文中，我们首先简要介绍了所谓的一般分数衍生物的主要特性，并在迄今为止引入了Sonin内核。这些是定义为一阶导数的组成和卷积类型的积分操作员的组合物。根据这些操作员的继承，对Riemann-Liouville和Caputo类型的一般分数衍生物进行了定义和研究。本文的主要目的是构造第一级的一般分数衍生物，既包括Riemann-Liouville类型的一般分数衍生物和Caputo类型的一般分数衍生物。我们还提供了一些属性，包括这些衍生物的分数演算的第一和第二基本定理以及适当定义的一般分数积分。
In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far. These are integro-differential operators defined as compositions of the first order derivative and an integral operator of convolution type. Depending on succession of these operators, the general fractional derivatives of the Riemann-Liouville and of the Caputo types were defined and studied. The main objective of this paper is a construction of the 1st level general fractional derivatives that comprise both the general fractional derivative of the Riemann-Liouville type and the general fractional derivative of the Caputo type. We also provide some of their properties including the 1st and the 2nd fundamental theorems of Fractional Calculus for these derivatives and the suitably defined general fractional integrals.
