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
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
. 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.
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Bazhlekova, E.; Bazhlekov, I. Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model. Fractal Fract 2017, 1, 7.
Bazhlekova E, Bazhlekov I. Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model. Fractal and Fractional. 2017; 1(1):7.
Bazhlekova, Emilia; Bazhlekov, Ivan. 2017. "Stokes’ First Problem for Viscoelastic Fluids with a Fractional Maxwell Model." Fractal Fract 1, no. 1: 7.
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