This　paper　presents　an　exact　solution　for　the　magnetohydrodynamic　(MHD)　flow　of　an　incompressible　generalized　Oldroyd-B　fluid　due　to　an　infinite　accelerating　plate.　The　fractional　calculus　approach　is　introduced　to　establish　the　constitutive　relationship　of　the　Oldroyd-B　fluid.　The　solutions　in　terms　of　Fox　H-function　are　obtained　by　using　the　Laplace　transform.　When　N　=　0　the　solutions　corresponds　to　the　generalized　Oldroyd-B　fluids,　while　θ　®→　and　λ　→0　describes　the　Maxwell　fluid　and　the　generalized　second　fluid,　as　limiting　cases　of　our　general　results,　respectively.　©　2015,　Global　Digital　Central.　All　rights　reserved.