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

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.