On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

By R. Bagley. 2007

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Creep, relaxation and viscosity properties for basic fractional models in rheology (2011, methodology): “aplace transform rule (A.8), the initial conditions do not appear in the Laplace domain. The equivalence of the two approaches was formerly outlined by Mainardi [26] and more recently noted by Bagley [1] for the fractional Zener model. We refer the reader to the paper by Heymans and Podubny [16] for”
Time-fractional derivatives in relaxation processes: a tutorial survey (2008, methodology): “Restricting our attention to a few significant papers published in the past century, let us quote the contributions by Bagley & Torvik [4, 6, 117], Caputo [14, 16, 18, 20, 25, 27], Friedrich & associates [40, 41, 42, 43, 44], Graffi [60], Gaul, Kempfle & associates [8, 45, 46, 47], Heymans [64], Koe”