Niels Henrik Abel and the birth of fractional calculus-Reference-Cited by-同舟云学术

Niels Henrik Abel and the birth of fractional calculus

Published:2017-10-01 Issue:5 Volume:20 Page:1068-1075
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Podlubny Igor¹,Magin Richard L.²,Trymorush Iryna¹

Affiliation:

1. Institute of Control and Informatization of Production Processes , BERG Faculty Technical University of Kosice , B. Nemcovej 3, 04200 Kosice , Slovakia

2. Department of Bioengineering , University of Illinois at Chicago , 851 S Morgan St, SEO 218 Chicago , IL 60607 , USA

Abstract

Abstract In his first paper on the generalization of the tautochrone problem, that was published in 1823, Niels Henrik Abel presented a complete framework for fractional-order calculus, and used the clear and appropriate notation for fractional-order integration and differentiation.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0057/pdf

Reference11 articles.

1. N.H. Abel, Oplösning af et par opgaver ved hjelp af bestemte integraler. Magazin for Naturvidenskaberne, Aargang I, Bind 2, Christiania, 1823. (Translation to French: N.H. Abel, Solution de quesques problèmes à l’aide d’intégrales définies. In: “Œ uvres complètes de Niels Henrik Abel. Nouvelle edition”, Edited by L. Sylow and S. Lie, Grøndahl & Søn, Christiania, 1881, Chapter II, pp. 11–27).

2. N.H. Abel, Auflösung einer mechanischen ausgabe. Journal für die Reine und Angewandte Mathematik, Band I, 153–157, Berlin, 1826. (Translation to French:

3. N.H. Abel, Resolution d’un problème de mécanique. In: “Œ uvres complètes de N.H. Abel”, Edited by B. Holmboe, Gröndahl, Christiania, 1839, Chapter IV, pp. 27–30;

4. N.H. Abel, Resolution d’un problème de mécanique. In: “Œ uvres complètes de Niels Henrik Abel. Nouvelle edition”, Edited by L. Sylow and S. Lie, Grøndahl & Søn, Christiania, 1881, Chapter IX, pp. 97–101).

5. A.-M. Legendre, Exercices de Calcul Intègral, Vol. 1. Coucier, Paris, 1811.

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