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Fractal Fract 2017, 1(1), 7; doi:10.3390/fractalfract1010007

Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, Sofia 1113, Bulgaria
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Received: 21 September 2017 / Revised: 20 October 2017 / Accepted: 23 October 2017 / Published: 24 October 2017
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering)
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Abstract

Stokes’ first problem for a class of viscoelastic fluids with the generalized fractional Maxwell constitutive model is considered. The constitutive equation is obtained from the classical Maxwell stress–strain relation by substituting the first-order derivatives of stress and strain by derivatives of non-integer orders in the interval ( 0 , 1 ] . Explicit integral representation of the solution is derived and some of its characteristics are discussed: non-negativity and monotonicity, asymptotic behavior, analyticity, finite/infinite propagation speed, and absence of wave front. To illustrate analytical findings, numerical results for different values of the parameters are presented. View Full-Text
Keywords: Riemann-Liouville fractional derivative; viscoelastic fluid; fractional Maxwell model; Stokes’ first problem; Mittag-Leffler function; Bernstein function Riemann-Liouville fractional derivative; viscoelastic fluid; fractional Maxwell model; Stokes’ first problem; Mittag-Leffler function; Bernstein function
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bazhlekova, E.; Bazhlekov, I. Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model. Fractal Fract 2017, 1, 7.

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