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

Fractal and Fractional

Bazhlekova, Emilia¹ 

关键词: Riemann-Liouville fractional derivative;    viscoelastic fluid;    fractional Maxwell model;    Stokes’ first problem;    Mittag-Leffler function;    Bernstein function;   

DOI  :  10.3390/fractalfract1010007

学科分类：数值分析

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY