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This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers' fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers' fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution.doi:10.21123/bsj.2020.17.1.0150 fatcat:lui55a2hgnhg5fqpuufji3e42q