Geodesic
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
Fractional calculus and applied analysis, Tome 10 (2007) no. 3, pp. 269-308

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The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into account initial conditions in the constitutive equations of fractional order. We also provide historical notes on the origins of the Caputo derivative and on the use of fractional calculus in viscoelasticity.
Keywords: Fractional Derivatives, Relaxation, Creep, Mittag-Leffler Function, Linear Viscoelasticity, 26A33, 33E12, 33C60, 44A10, 45K05, 74D05 
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Mainardi, Francesco; Gorenflo, Rudolf. Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey. Fractional calculus and applied analysis, Tome 10 (2007) no. 3, pp. 269-308. http://geodesic.mathdoc.fr/item/FCAA_2007_10_3_a2/