Time-fractional derivatives in relaxation processes: a tutorial survey

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dc.creatorMainardi, Francesco
dc.creatorGorenflo, Rudolf
dc.date2008-01-31
dc.date.accessioned2026-07-07T09:39:13Z
dc.date.available2026-07-07T09:39:13Z
dc.descriptionThe 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 classical theory of linear viscoelasticity, we contrast these two types of fractional 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.
dc.description40 pages, 5 Figures
dc.identifierhttps://arxiv.org/abs/0801.4914
dc.identifierhttp://arxiv.org/abs/0801.4914
dc.identifierFractional Calculus and Applied Analysis,Vol. 10 No 3 (2007) pp. 269-308
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161089
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectDynamical Systems
dc.subject26A33, 33E12, 33C60, 44A10 (Primary); 45K05, 74D05 (Secondary)
dc.titleTime-fractional derivatives in relaxation processes: a tutorial survey
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