How Many Fractional Derivatives Are There?

Duarte Valério, Manuel D. Ortigueira, António M. Lopes

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)
250 Downloads (Pure)


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.

Original languageEnglish
Article number737
Number of pages18
Issue number5
Publication statusPublished - 25 Feb 2022


  • fractional calculus
  • fractional derivative
  • signals and systems


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