# Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Rossikhin, Yuriy; Shitikova, Marina

Fractional Calculus and Applied Analysis (2007)

- Volume: 10, Issue: 2, page 111-121
- ISSN: 1311-0454

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topRossikhin, Yuriy, and Shitikova, Marina. "Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders." Fractional Calculus and Applied Analysis 10.2 (2007): 111-121. <http://eudml.org/doc/11320>.

@article{Rossikhin2007,

abstract = {Mathematics Subject Classification: 74D05, 26A33In 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.∗ This paper has been partially supported by the Russian Foundation for Basic Research under Grant No. 05-08-17936.},

author = {Rossikhin, Yuriy, Shitikova, Marina},

journal = {Fractional Calculus and Applied Analysis},

keywords = {74D05; 26A33},

language = {eng},

number = {2},

pages = {111-121},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders},

url = {http://eudml.org/doc/11320},

volume = {10},

year = {2007},

}

TY - JOUR

AU - Rossikhin, Yuriy

AU - Shitikova, Marina

TI - Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

JO - Fractional Calculus and Applied Analysis

PY - 2007

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 10

IS - 2

SP - 111

EP - 121

AB - Mathematics Subject Classification: 74D05, 26A33In 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.∗ This paper has been partially supported by the Russian Foundation for Basic Research under Grant No. 05-08-17936.

LA - eng

KW - 74D05; 26A33

UR - http://eudml.org/doc/11320

ER -

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