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Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1319

Title: Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
Authors: Mainardi, Francesco
Gorenflo, Rudolf
Keywords: Fractional Derivatives
Relaxation
Creep
Mittag-Leffler Function
Linear Viscoelasticity
26A33
33E12
33C60
44A10
45K05
74D05
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 3, (2007), 269p-308p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,
URI: http://hdl.handle.net/10525/1319
ISSN: 1311-0454
Appears in Collections:2007

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