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 viscous-diffusion 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.
Application of Fractional Calculus to Fluid Mechanics
Contributed by the Fluids Engineering Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the Fluids Engineering Division October 13, 1999; revised manuscript received February 18, 2002. Associate Editor: U. Ghia.
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Kulish, V. V., and Lage, J. L. (August 19, 2002). "Application of Fractional Calculus to Fluid Mechanics." ASME. J. Fluids Eng. September 2002; 124(3): 803–806. https://doi.org/10.1115/1.1478062
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