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Open AccessArticle

On Fractional Operators and Their Classifications

1
Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
2
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
3
Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99628 Famagusta, Northern Cyprus, via Mersin-10, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 830; https://doi.org/10.3390/math7090830
Received: 22 June 2019 / Revised: 3 September 2019 / Accepted: 6 September 2019 / Published: 8 September 2019
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
Fractional calculus dates its inception to a correspondence between Leibniz and L’Hopital in 1695, when Leibniz described “paradoxes” and predicted that “one day useful consequences will be drawn” from them. In today’s world, the study of non-integer orders of differentiation has become a thriving field of research, not only in mathematics but also in other parts of science such as physics, biology, and engineering: many of the “useful consequences” predicted by Leibniz have been discovered. However, the field has grown so far that researchers cannot yet agree on what a “fractional derivative” can be. In this manuscript, we suggest and justify the idea of classification of fractional calculus into distinct classes of operators. View Full-Text
Keywords: fractional calculus; integral transforms; convergent series fractional calculus; integral transforms; convergent series
MDPI and ACS Style

Baleanu, D.; Fernandez, A. On Fractional Operators and Their Classifications. Mathematics 2019, 7, 830. https://doi.org/10.3390/math7090830

AMA Style

Baleanu D, Fernandez A. On Fractional Operators and Their Classifications. Mathematics. 2019; 7(9):830. https://doi.org/10.3390/math7090830

Chicago/Turabian Style

Baleanu, Dumitru; Fernandez, Arran. 2019. "On Fractional Operators and Their Classifications" Mathematics 7, no. 9: 830. https://doi.org/10.3390/math7090830

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