What is a fractional derivative?

Ortigueira, Manuel; Machado, J. A. Tenreiro

http://hdl.handle.net/10400.22/6952

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Authors

Ortigueira, Manuel

Machado, J. A. Tenreiro

Abstract(s)

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.