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This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at    $$y=0$$  y = 0 , while the plate at    $$y=d$$  y = d is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE’s are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick’s and Fourier’s Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter    $$\lambda$$  λ deaccelerate the velocity of Couple stress Casson fluid.

Time fractional analysis of channel flow of couple stress Casson fluid using Fick’s and Fourier’s Laws