Analytical solutions of fractional couple stress fluid flow for an engineering problem

Abstract In this article, analytical solutions of couple stress fluid flow modeled with a power law fractional differential operator are discussed. Stokes’ second problem for an incompressible couple stress fluid is studied for an horizontal plate of infinite length. The governing equations of the flow problem are expressed in terms of a partial differential operator and then converted into a non-dimensional model by using dimensional analysis. Then the integer order problem was formulated in terms of the non-integer order of three types of fractional derivatives and then solved with the help of the Laplace transform method. The obtained solutions are complex and expressed in terms of series. In order to check the memory index of the solutions obtained with three different fractional operators, we have plotted some graphs. It is found that the constant proportional operator provides us a better choice about the memory and maximum enhancement achieved in the comparison of Caputo and Caputo–Fabrizio. Furthermore, in order to check the accuracy of the present results, we have compared the obtained solutions with the existing literature and found a good agreement between them.