论文标题
关于有争议的问题的评论：广义的分数衍生物不能具有常规内核
A comment on a controversial issue: a Generalized Fractional Derivative cannot have a regular kernel
论文作者
论文摘要
一个给定的函数是否可以用作广义分数衍生物的内核和相关的广义分数积分的问题降低到存在解决方案的解决方案的问题。对于某些选定的函数类别显示，函数成为分数导数的内核的必要条件是在0处的可集成奇异性。这表明局部可完全集成的完全单调的单调函数在0时仅在0时满足sonine方程。
The problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the problem of existence of a solution to the Sonine equation. It is shown for some selected classes of functions that a necessary condition for a function to be the kernel of a fractional derivative is an integrable singularity at 0. It is shown that locally integrable completely monotone functions satisfy the Sonine equation if and only if they are singular at 0.
