Niels Henrik Abel and the birth of fractional calculus

TL;DR

This paper explores Niels Henrik Abel's pioneering work that laid the foundation for fractional calculus, including translations of his key papers and historical context, highlighting his influence on modern mathematical analysis.

Contribution

It provides English translations of Abel's original papers and contextualizes his role in the development of fractional calculus, preserving original notation and historical significance.

Findings

Translations of Abel's key papers are provided.

Historical development of fractional calculus is detailed.

Original mathematical notation is preserved.

Abstract

This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with the supplements to it. Hereby translation to English of the first part of the important Abel's paper (Abel, N. H., Oplosning af et par opgaver ved hjelp af bestemte integraler, Magazin for Naturvidenskaberne, Aargang I, Bind 2, Christiania, 1823) and another important Abel's paper (Abel, N. H., Auflosung einer mechanischen ausgabe. Journal fur die Reine und Angewandte Mathematik, Bind I, 153-157, Berlin, 1826) are provided. To preserve the original flavor and the historical development of mathematical notation, the formulas are typeset in the original manner.