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Open AccessArticle

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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Fractal Fract 2017, 1(1), 7; https://doi.org/10.3390/fractalfract1010007
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)
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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Bazhlekova, E.; Bazhlekov, I. Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model. Fractal Fract 2017, 1, 7.

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