On Fractional Operators and Their Classifications

Dumitru Baleanu and Arran Fernandez
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Dumitru Baleanu: Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey
Arran Fernandez: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99628 Famagusta, Northern Cyprus, via Mersin-10, Turkey

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: 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.

Keywords: fractional calculus; integral transforms; convergent series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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