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.
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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).
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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).
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Podlubny, I., Magin, R.L. & Trymorush, I. Niels Henrik Abel and the birth of fractional calculus. FCAA 20, 1068–1075 (2017). https://doi.org/10.1515/fca-2017-0057
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DOI: https://doi.org/10.1515/fca-2017-0057