What is a fractional derivative?

Manuel D. Ortigueira, J. A. Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

294 Citations (Scopus)


This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Original languageEnglish
Pages (from-to)4-13
Number of pages10
JournalJournal of Computational Physics
Issue numberSI
Publication statusPublished - Jul 2015


  • Fractional calculus
  • Fractional derivative
  • Riesz potential


Dive into the research topics of 'What is a fractional derivative?'. Together they form a unique fingerprint.

Cite this