Fractional integral and fractional differential equations in fluid mechanics. (English) Zbl 1076.35095

Debnath, Lokenath

Fract. Calc. Appl. Anal. 6, No. 2, 119-155 (2003).

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:

35Q35	PDEs in connection with fluid mechanics
26A33	Fractional derivatives and integrals
35A22	Transform methods (e.g., integral transforms) applied to PDEs

Keywords:

fractional diffusion-wave equation; Green’s function; fractional Schrödinger equation; Laplace transform; Fourier transform