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In the present article, we intend to solve the Stokes first and second problems for an incompressible couple stress fluid under isothermal conditions. The solutions of the considered problems are obtained by the Laplace transform (LT) as for the time variable $t$ and the sine Fourier transform (FT) as for the $y$-variable. It ought be noticed that by suitable manipulations of the inverse integral transforms, fluid velocity expressions are written as the sum of steady-state (post-transient solution) and transient solutions. Further, we wish to give a comparison of the obtained results and the results obtained by Devakar and Lyengar \cite{1} by using the four inverse Laplace transform algorithms (Stehfests, Tzous, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for different times and different values of couple stress Reynolds number. At the end, the outcomes are introduced through graphs and in tabular forms.

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