Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1309

 Title: Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders Authors: Rossikhin, YuriyShitikova, Marina Keywords: Fractional DerivativeFractional Exponential FunctionRabotnov's Hereditarity Elastic Medium74D0526A33 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 URI: http://hdl.handle.net/10525/1309 ISSN: 1311-0454 Appears in Collections: 2007

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