Fractional Derivatives: The Perspective of System Theory

Manuel Duarte Ortigueira and José Tenreiro Machado
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Manuel Duarte Ortigueira: 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
José Tenreiro Machado: Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal

Mathematics, 2019, vol. 7, issue 2, 1-14

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.

Keywords: fractional calculus; fractional derivatives; fractional anti-derivatives; fractional integrals; fractional operators (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 (5)

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