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Mathematics 2019, 7(2), 150; https://doi.org/10.3390/math7020150

Fractional Derivatives: The Perspective of System Theory

1
CTS–UNINOVA and DEE of NOVA, School of Science and Technology, Nova University of Lisbon, Campus da FCT da UNL, Quinta da Torre, 2829–516 Caparica, Portugal
2
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal
*
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 21 January 2019 / Accepted: 25 January 2019 / Published: 5 February 2019
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
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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. View Full-Text
Keywords: fractional calculus; fractional derivatives; fractional anti-derivatives; fractional integrals; fractional operators fractional calculus; fractional derivatives; fractional anti-derivatives; fractional integrals; fractional operators
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Duarte Ortigueira, M.; Tenreiro Machado, J. Fractional Derivatives: The Perspective of System Theory. Mathematics 2019, 7, 150.

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