This　work　is　concerned　the　flow　of　a　generalized　Oldroyd-B　fluid　in　a　porous　half-space　with　second-order　slip　effect.　The　fractional　calculus　approach　is　used　to　establish　the　constitutive　relationship　of　the　non-Newtonian　fluid　model.　A　new　motion　model　is　firstly　proposed　by　modifying　the　boundary　condition　with　second-order　slip　effect.　Exact　solutions　for　velocity　and　shear　stress　are　obtained　in　terms　of　Fox　H-function　by　using　the　discrete　inverse　Laplace　transform　of　the　sequential　fractional　derivatives.　The　similar　solutions　for　the　generalized　Oldroyd-B　fluid　with　first-order　slip　or　no　slip,　and　the　solutions　for　a　generalized　Oldroyd-B　fluid　in　nonporous　medium,　are　obtained　as　the　limiting　cases　of　our　solutions.　Furthermore,　the　behavior　of　various　parameters　on　the　corresponding　flow　characteristics　is　shown　graphical　through　different　diagrams.