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Zbl 1076.35095
Debnath, Lokenath
Fractional integral and fractional differential equations in fluid mechanics. (English)
[J] Fract. Calc. Appl. Anal. 6, No. 2, 119-155 (2003). ISSN 1311-0454; ISSN 1314-2224/e

Summary: This paper is concerned with some basic properties of the classical and modern definitions of fractional derivatives and fractional integrals. Special attention is paid to recent examples of applications in fractional ordinary differential equations, fractional partial differential equations, and fractional integral equations. Several examples of fractional partial differential equations in fluid mechanics are presented. Included are Green's functions of fractional differential equations and fractional Schrödinger equation in quantum mechanics.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
26A33 Fractional derivatives and integrals (real functions)
35A22 Transform methods (PDE)

Keywords: fractional diffusion-wave equation; Green's function; fractional Schrödinger equation; Laplace transform; Fourier transform

Cited in: Zbl 1211.26009 Zbl 1190.65157

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