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 Gfunctions, 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. (2000). 76A05. Mathematics Subject Classification

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a b s t r a c tThe helical flow of an Oldroyd-B fluid with fractional derivatives, also named generalized Oldroyd-B fluid, in an infinite circular cylinder is studied using Hankel and Laplace transforms. The motion is due to the cylinder that, at time t = 0 + begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Vt.The components of the velocity field and the resulting shear stresses are presented under integral and series form in terms of the generalized G and R functions. The solutions that have been obtained satisfy all imposed initial and boundary conditions, and are presented as sums of two terms, one of them being a similar solution for a Newtonian fluid. Similar solutions for generalized Maxwell fluids, as well as those for ordinary Oldroyd-B and Maxwell fluids are obtained as limiting cases of our general solutions. Furthermore, the solutions for Newtonian fluids performing the same motion, are also obtained as special cases of our solutions for α = β = 1 and λ r → λ.

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