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.