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Zbl 1157.26304
Mainardi, Francesco; Gorenflo, Rudolf
Time-fractional derivatives in relaxation processes: a tutorial survey. (English)
[J] Fract. Calc. Appl. Anal. 10, No. 3, 269-308 (2007). ISSN 1311-0454; ISSN 1314-2224/e

Summary: 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 Riemann-Liouville sense arid 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 oil the origin's of the Caputo derivative and on the use of fractional calculus in viscoelasticity.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
33E12 Mittag-Leffler functions and generalizations
33C60 Hypergeometric integrals and functions defined by them
44A10 Laplace transform
45K05 Integro-partial differential equations
74D05 Linear constitutive equations

Keywords: fractional derivatives; relaxation; creep; Mittag-Leffler function; linear viscoelasticity

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Zentralblatt MATH Berlin [Germany]