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This article leads to free convection problem of magnetohydrodynamic second grade fluid with porous medium using recently defined Caputo-Fabrizoi fractional derivatives. Analytical expressions for temperature distribution and velocity field have been investigated using Laplace transforms having inverses. The general expressions for Temperature distribution and velocity field are written in terms of Generalized Mittage-Leffler function MP Q,R(Z) and Fox-H function H 1,P P,Q+1(Z) respectively. Both the solutions of Temperature distribution and velocity field satisfy implemented conditions as V (y, 0) = T(y, 0) = 0 and V (0, t) = UH(t)cos(ωt), V (0, t) = UH(t)sin(ωt) and T(0, t) = 1. The general expressions have been reduced for limiting cases. Finally influences of material parameter, non-dimensional parameters, rheological parameters and Caputo-Fabrizoi fractional parameter are analyzed graphically by choosing distinct values on fluid flow.