Fractional derivatives: The perspective of system theory

Manuel Duarte Ortigueira; José Tenreiro Machado

doi:10.3390/math7020150

Fractional derivatives: The perspective of system theory

Manuel Duarte Ortigueira, José Tenreiro Machado

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Abstract

This paper addresses the present day problem of multiple proposals for operators under the umbrella of "fractional derivatives". Several papers demonstrated that various of those "novel" definitions are incorrect. Here the classical system theory is applied to develop a unified framework to clarify this important topic in Fractional Calculus.

Original language	English
Article number	150
Journal	Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.3390/math7020150
Publication status	Published - 5 Feb 2019

Keywords

Fractional anti-derivatives
Fractional calculus
Fractional derivatives
Fractional integrals
Fractional operators

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10.3390/math7020150Licence: CC BY

Fractional DerivativesThe Perspective of System TheoryFinal published version, 358 KBLicence: CC BY

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title = "Fractional derivatives: The perspective of system theory",

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keywords = "Fractional anti-derivatives, Fractional calculus, Fractional derivatives, Fractional integrals, Fractional operators",

author = "Ortigueira, {Manuel Duarte} and Machado, {Jos{\'e} Tenreiro}",

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KW - Fractional derivatives

KW - Fractional integrals

KW - Fractional operators

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Fractional derivatives: The perspective of system theory

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Keywords

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