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Desiderata for Fractional Derivatives and Integrals

by Rudolf Hilfer 1 and Yuri Luchko 2,*
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.
Mathematics 2019, 7(2), 149;
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”)
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
MDPI and ACS Style

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

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