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Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics. (English) Zbl 1076.35096
Summary: This paper deals with the solutions of linear inhomogeneous fractional partial differential equations in applied mathematics and fluid mechanics. These equations include the general inhomogeneous fractional evolution equation, the linear Klein-Gordon equation, the linear telegraph equation, and the linear fractional Stokes-Ekman equation in geophysical fluid dynamics. Solutions to some linear fractional inhomogeneous equations such as linearised versions of fractional Burgers equations, Korteweg-de Vries (KdV) equations, KdV-Burgers equations are obtained from the solution of the general evolution equation. This is followed by the fractional order linear shallow water equations in a uniformly rotating ocean. The Laplace transform method is used to solve the above inhomogeneous fractional differential equations. It is shown that the corresponding solutions of the integer order partial differential equations follow as special cases of those of fractional partial differential equations.

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