Effect of fractional time derivatives to pressure-driven flow through the horizontal microchannel

This research applies fractional time derivatives to fluid flow through a horizontal microchannel. It uses fractional time derivatives with the Laplace transform technique and method of undetermined coefficient to analyze and obtain solutions of the governing equations in the Laplace domain. To this end, the solutions are reversed in the time domain using Riemann-sum approximation methods. In order to obtain the solutions for the pressure-driven flow, the time factional derivative in the Caputo sense is employed. Here, the influence of each governing parameter is explained with a line graph. Results show that with the decreases in fractional order $(\\alpha)$, the velocity decreases within the interval $0<\\alpha<1$. The fluid velocity increases and decreases as the Knudsen number $(kn)$ changes. Besides, transient wall-skin frictions for different times $(t)$ and Knudsen number $(kn)$ with a fixed value of fractional order $(\\alpha)$ are observed.