论文标题
加权分数演算：一般运算符类
Weighted fractional calculus: a general class of operators
论文作者
论文摘要
分数演算的运算符有许多不同类型的类型，可以根据其性质和属性将其分为一般类别。我们对称为加权分数演算的类别进行了正式研究，并将其扩展到较大的较大类，称为加权分数演算相对于功能。这些类别包含钢化，哈达玛型和erdélyi的特殊情况，通常它们可以通过共轭关系与经典的riemann-liouville分数演算有关。考虑到拉普拉斯变换和卷积操作的相应修改，可以在这些通用类操作员的设置中解决微分方程。
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its extension to the larger class known as weighted fractional calculus with respect to functions. These classes contain tempered, Hadamard-type, and Erdélyi--Kober operators as special cases, and in general they can be related to the classical Riemann--Liouville fractional calculus via conjugation relations. Considering the corresponding modifications of the Laplace transform and convolution operations enables differential equations to be solved in the setting of these general classes of operators.
