Ortigueira, ManuelMachado, J. A. Tenreiro2015-11-192015-11-192015http://hdl.handle.net/10400.22/6952This 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.engFractional derivativeRiesz potentialFractional calculusjournal article10.1016/j.jcp.2014.07.019