Application of Fractional Calculus to Fluid Mechanics (original) (raw)

2002, Journal of Fluids Engineering-transactions of The Asme

In this note we present the application of fractional calculus, or the calculus of arbitrary (noninteger) differentiation, to the solution of time-dependent, viscous-diffusion fluid mechanics problems. Together with the Laplace transform method, the application of fractional calculus to the classical transient viscousdiffusion equation in a semi-infinite space is shown to yield explicit analytical (fractional) solutions for the shear-stress and fluid speed anywhere in the domain. Comparing the fractional results for boundary shear-stress and fluid speed to the existing analytical results for the first and second Stokes problems, the fractional methodology is validated and shown to be much simpler and more powerful than existing techniques. Fig. 1 Time evolution of surface shear stress, Eq. "21…, and the imposed boundary condition "dashed line…: U"t…ÕUÄsin"t….

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