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The present study is analyzed for slippage of velocity field and shear stress for accelerating flows of magnetohydrodynamics Oldroyd-B fluid in presence of porosity. The analytical solutions have been obtained by employing fractional derivative approach on the governing partial differential equations. The expressions of general solutions have been presented in terms of newly defined M p q function. These solutions are verified for initial and boundary conditions. Some special cases of fluid are particularized for ordinary Oldroyd-B, fractionalized and ordinary Maxwell, fractionalized and ordinary second grade and also for Newtonian fluids with respect to fractional parameters α , γ , λ r, λ , β , ρ ,t, θ , µ , ν , p and Φ . The influence of rheological and fractional parameters is analyzed through graphical illustrations and depicted in with and without slippage.

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