Application of Fractional Calculus to Fluid Mechanics-Reference-Cited by-同舟云学术

Application of Fractional Calculus to Fluid Mechanics

Published:2002-08-19 Issue:3 Volume:124 Page:803-806
ISSN:0098-2202
Container-title:Journal of Fluids Engineering
language:en
Short-container-title:

Author:

Kulish Vladimir V.¹,Lage Jose´ L.²

Affiliation:

1. School of Mechanical and Production Engineering, Nanyang Technological University, Singapore 639798

2. Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75275-0337

Abstract

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.

Publisher

ASME International

Subject

Mechanical Engineering

Link

http://asmedigitalcollection.asme.org/fluidsengineering/article-pdf/124/3/803/5902859/803_1.pdf

Reference22 articles.

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2. Liouville, J. , 1932, “Me´moie: Sur le calcul des diffe´rentielles a` indices quelconques,” Journal Ecole Polytechniuqe, 13, p. 7171.

3. Riemann, B., 1953, “Versuch einer allgemeinen Auffasung der Integration und Differentiation,” The Collected Works of Bernhard Riemann, H. Weber, ed., 2nd ed., Dover, New York.

4. Holmgren, H. J. , 1864, “Om differentialkalkylen med indices of hvad nature sam helst,” Kgl. Sv. Vetenskapsakademia Handl, 11, p. 11.

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