Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the thermodynamical restrictions in isothermal deformations of fractional Burgers model
Journal: Philosophical Transactions of the Royal Society. A: Mathematical, Physical and Engineering Sciences
Volume: 378
Issue: 2172
First page: 20190278
Issue Date: 29-May-2020
Rank: M21
ISSN: 1364-503X
DOI: 10.1098/rsta.2019.0278
Abstract: 
We investigate, in the distributional setting, the restrictions on the constitutive equation for a fractional Burgers model of viscoelastic fluid that follow from the weak form of the entropy inequality under isothermal conditions. The results are generalized, from the Burgers model, to an arbitrary class of linear constitutive equations with fractional derivatives. Our results show that the restrictions obtained here on the coefficients of constitutive equations are weaker when compared with the restrictions obtained by Bagley-Torvik method. We show the precise relation between restrictions derived here and those derived by Bagley-Torvik. We deal with the creep test, for the case when Bagley-Torvik conditions are violated, and new conditions obtained in this work are satisfied. The results show a qualitative difference in the form of creep function. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
Keywords: Bochner–Schwartz theorem | dissipativity condition | fractional burgers model
Publisher: The Royal Society Publishing
Project: Development of Dialogue Systems for Serbian and Other South Slavic Languages 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Methods of Functional and Harmonic Analysis and PDE with Singularities 

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