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Fractal Fract
Volume 4
Issue 3
10.3390/fractalfract4030040
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Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive?

by
Jocelyn Sabatier
IMS Laboratory, Bordeaux University, UMR 5218 CNRS, 351 Cours de la Libération, 33405 Talence, France
Fractal Fract. 2020, 4(3), 40; https://doi.org/10.3390/fractalfract4030040
Submission received: 13 June 2020 / Revised: 31 July 2020 / Accepted: 3 August 2020 / Published: 11 August 2020
(This article belongs to the Special Issue 2020 Selected Papers from Fractal Fract’s Editorial Board Members)
Versions Notes

Abstract

In the field of fractional calculus and applications, a current trend is to propose non-singular kernels for the definition of new fractional integration and differentiation operators. It was recently claimed that fractional-order derivatives defined by continuous (in the sense of non-singular) kernels are too restrictive. This note shows that this conclusion is wrong as it arises from considering the initial conditions incorrectly in (partial or not) fractional differential equations.
Keywords: fractional derivative; continuous kernel; Volterra equation; fractional models’ initialization; distributed time delay systems fractional derivative; continuous kernel; Volterra equation; fractional models’ initialization; distributed time delay systems

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MDPI and ACS Style

Sabatier, J. Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive? Fractal Fract. 2020, 4, 40. https://doi.org/10.3390/fractalfract4030040

AMA Style

Sabatier J. Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive? Fractal and Fractional. 2020; 4(3):40. https://doi.org/10.3390/fractalfract4030040

Chicago/Turabian Style

Sabatier, Jocelyn. 2020. "Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive?" Fractal and Fractional 4, no. 3: 40. https://doi.org/10.3390/fractalfract4030040

APA Style

Sabatier, J. (2020). Fractional-Order Derivatives Defined by Continuous Kernels: Are They Really Too Restrictive? Fractal and Fractional, 4(3), 40. https://doi.org/10.3390/fractalfract4030040

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