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

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.


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