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Mathematics 2018, 6(1), 3; https://doi.org/10.3390/math6010003

Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives

Department of Economics, Belarusian State University, 4, Nezavisimosti ave, 220030 Minsk, Belarus
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Received: 22 November 2017 / Revised: 14 December 2017 / Accepted: 20 December 2017 / Published: 25 December 2017
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
Full-Text   |   PDF [258 KB, uploaded 25 December 2017]

Abstract

In this survey paper, we analyze two constructions of fractional derivatives proposed by Aleksey Letnikov (1837–1888) and by André Marchaud (1887–1973), respectively. These derivatives play very important roles in Fractional Calculus and its applications. View Full-Text
Keywords: fractional integrals and derivatives; Grünwald–Letnikov approach; Marchaud approach; fractional differences; Hadamard finite part fractional integrals and derivatives; Grünwald–Letnikov approach; Marchaud approach; fractional differences; Hadamard finite part
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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Rogosin, S.; Dubatovskaya, M. Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives. Mathematics 2018, 6, 3.

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