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Mathematics 2018, 6(1), 6; https://doi.org/10.3390/math6010006

Weyl and Marchaud Derivatives: A Forgotten History

Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Dedicated to Sandro Salsa for his 68th birthday.
Received: 22 November 2017 / Revised: 23 December 2017 / Accepted: 29 December 2017 / Published: 3 January 2018
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
Full-Text   |   PDF [304 KB, uploaded 3 January 2018]

Abstract

In this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics. View Full-Text
Keywords: fractional derivatives; Grünwald–Letnikov derivative; Weyl derivative; Marchaud derivative; fractional Laplace operator; extension operator fractional derivatives; Grünwald–Letnikov derivative; Weyl derivative; Marchaud derivative; fractional Laplace operator; extension operator
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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Ferrari, F. Weyl and Marchaud Derivatives: A Forgotten History. Mathematics 2018, 6, 6.

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