| Summary: | This work explores the effect of second order slip on magnetohydrodynamic (MHD) flow of a fractional Maxwell fluid on a moving plate and a comparison between two numerical algorithms (Tzou and Stehfest’s algorithm). The problem is formulated for Maxwell fluid with Caputo-time fractional derivatives. Semi analytical solutions are derived using Laplace transform. The solution is obtained using numerical technique of Laplace transform Stehfest’s algorithm. To insight the physical behavior of the fluid, a graphical illustration is made. The influence of fractional parameter, the magnetic force, the porosity parameter, the slip parameters are analyzed and discussed. A tabular and graphical comparisons with Tzou’s algorithm are made for the sake of validation of the present results. Keywords: Fractional Maxwell fluid, Porous medium, Second order slip, Numerical Laplace inverse
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