A comment on a controversial issue: A generalized fractional derivative cannot have a regular kernel-Reference-Cited by-同舟云学术

A comment on a controversial issue: A generalized fractional derivative cannot have a regular kernel

Published:2020-02-01 Issue:1 Volume:23 Page:211-223
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Hanyga Andrzej¹

Affiliation:

1. Emeritus, Polish Academy of Sciences and ul. Bitwy Warszawskiej 1920r 14/52, 02-366 , Warszawa , Poland

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0008/pdf

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