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

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.

Keywords

• Riemann-Liouville fractional derivative
• viscoelastic fluid
• fractional Maxwell model
• Stokes’ first problem
• Mittag-Leffler function
• Bernstein function