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Mathematics 2019, 7(2), 149;

Desiderata for Fractional Derivatives and Integrals

ICP, Fakultät für Mathematik und Physik, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
Fachbereich Mathematik-Physik-Chemie, Beuth Hochschule für Technik Berlin, Luxemburger Str. 10, 13353 Berlin, Germany
Author to whom correspondence should be addressed.
Received: 11 January 2019 / Revised: 24 January 2019 / Accepted: 25 January 2019 / Published: 4 February 2019
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
Full-Text   |   PDF [250 KB, uploaded 4 March 2019]


The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria. View Full-Text
Keywords: fractional derivatives; fractional integrals; fractional calculus fractional derivatives; fractional integrals; fractional calculus
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Hilfer, R.; Luchko, Y. Desiderata for Fractional Derivatives and Integrals. Mathematics 2019, 7, 149.

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