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A new fractional Navier–Stokes equation is constructed based on the notion of fractional velocity recently introduced in the literature. Its implications in fluid mechanics were discussed. In particular, the Couette and the Poiseuille flows and some insights of fluid flow in microfilaments were addressed accordingly.

Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments