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Zbl 1076.35096
Debnath, Lokenath; Bhatta, Dambaru D.
Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics. (English)
[J] Fract. Calc. Appl. Anal. 7, No. 1, 21-36 (2004). ISSN 1311-0454; ISSN 1314-2224/e

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.

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

Keywords: Klein-Gordon equation; telegraph equation; Stokes-Ekman equation; Burgers equation; KdV-Burgers equation; shallow water equations; Laplace transform

Cited in: Zbl 1134.35093 Zbl 1157.35082

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