How Many Fractional Derivatives Are There?

Duarte Valério, Manuel D. Ortigueira and António M. Lopes
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Duarte Valério: IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Manuel D. Ortigueira: Centre of Technology and Systems–UNINOVA and Department of Electrical Engineering, NOVA School of Science and Technology of NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
António M. Lopes: LAETA/INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal

Mathematics, 2022, vol. 10, issue 5, 1-18

Abstract: In this paper, we introduce a unified fractional derivative , defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We consider also some myths of Fractional Calculus and false fractional derivatives. The results are expected to contribute to limit the appearance of derivatives that differ from existing ones just because they are defined on distinct domains, and to prevent the ambiguous use of the concept of fractional derivative.

Keywords: fractional calculus; fractional derivative; signals and systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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