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On Fractional Operators and Their Classifications

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Date

2019

Authors

Baleanu, Dumitru
Fernandez, Arran

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MDPI

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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.

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Fractional Calculus, Integral Transforms, Convergent Series

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Citation

Baleanu, Dumitru; Fernandez, Arran, "On Fractional Operators and Their Classifications", Mathematics, Vol. 7, No. 9, (September 2019).

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Mathematics

Volume

7

Issue

9

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