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Title: Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders
Authors: Rossikhin, Yuriy
Shitikova, Marina
Keywords: Fractional Derivative
Fractional Exponential Function
Rabotnov's Hereditarity Elastic Medium
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 2, (2007), 111p-121p
Abstract: In this paper, a comparative analysis of the models involving fractional derivatives of di®erent orders is given. Such models of viscoelastic materials are widely used in various problems of mechanics and rheology. Rabotnov's hereditarily elastic rheological model is considered in detail. It is shown that this model is equivalent to the rheological model involving fractional derivatives in the stress and strain with the orders proportional to a certain positive value less than unit. In the scienti¯c literature such a model is referred to as Koeller's model. Inversion of Rabotnov's model developed by himself based on algebra of operators results in similar rheological dependences. Inversion of Koeller's model carried out using Miller's theorem coincides inherently with Rabotnov's inversion procedure.
Description: Mathematics Subject Classification: 74D05, 26A33
ISSN: 1311-0454
Appears in Collections:2007

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