Z. angew. Math. Phys. 60 (2009) 921–933 0044-2275/09/050921-13 DOI 10.1007/s00033-008-8055-5 c  2008 Birkh¨auser Verlag, Basel Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid Corina Fetecau ∗ , Muhammad Jamil, Constantin Fetecau and Dumitru Vieru Abstract. The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G- functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique. Mathematics Subject Classification (2000). 76A05. Keywords. Rayleigh–Stokes problem, generalized Oldroyd-B fluid, velocity field. 1. Introduction In the last time, the fractional calculus has encountered much success in the de- scription of viscoelasticity. Especially, the rheological constitutive equations with fractional derivatives play an important role in description of the behavior of the polymer solutions and melts. The starting point of a fractional derivative model is usually a classical differential equation which is modified by replacing the time derivative of an integer order by so-called Rieman–Liouville fractional differential operator. More exactly, these equations are derived from the well-known models (the Oldroyd-B model, for instance) by substituting the ordinary derivatives of first, second and higher order by fractional derivatives of non-integer order [1]. In some cases, the constitutive equations employing the fractional derivatives are also linked to molecular theories [2]. At least the modified viscoelastic models are appropriate to describe the behavior for Xantan gum and Sesbonia gel [3]. * Author of correspondence.