The　Rayleigh-Stokes　problem　for　a　generalized　second　grade　fluid　subject　to　a　flow　on　a　heated　plate　and　within　a　heated　edge　was　investigated.　For　description　of　such　a　viscoelastic　fluid,　fractional　calculus　approach　in　the　constitutive　relationship　model　was　used.　Exact　solutions　of　the　velocity　and　temperature　fields　were　obtained　using　the　Fourier　sine　transform　and　the　fractional　Laplace　transform.　The　well-known　solutions　of　the　Stokes＇　first　problem　for　a　viscous　Newtonian　fluid,　as　well　as　those　corresponding　to　a　second　grade　fluid,　appear　in　limiting　cases　of　our　results.　(c)　2005　Elsevier　Ltd.　All　rights　reserved.