Abstract
This paper presents a research for the magnetohydrodynamic (MHD) flow of an incompressible generalized Oldroyd-B fluid due to an infinite accelerating plate. The motion of the fluid is produced by the infinite plate, which at time t = 0 + begins to slide in its plane with a velocity A t . The fractional calculus approach is introduced to establish the constitutive relationship of the Oldroyd-B fluid. The solutions are established by means of Fourier sine and Laplace transforms in terms of the G and R functions written as a direct sum of the Newtonian solution and the corresponding non-Newtonian solutions. When α = β = 1 , M = 0 , the solutions corresponds to the ordinary Oldroyd-B fluids, while θ = 0 and λ = 0 describe the Maxwell fluid and the generalized second grade fluid, as limiting cases of present results, respectively.
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