Title: Solving k-fractional shallow water wave equations via homotopy analysis transform method

Authors: Youwei Zhang

Addresses: Department of Mathematics, Hexi University, Beihuan Road 87, 734000 Zhangye, Gansu, P.R. China

Abstract: In this paper, homotopy analysis transform method has been applied to obtain the approximate analytical solution of the shallow water equations with time-fractional derivatives. The interesting point is manifested in its emphatic application of k-fractional Riemann-Liouville time derivatives on the classical equations with an achievement of the highly accurate solutions by the known series solutions.

Keywords: approximate analytical solution; fractional shallow water wave equations; homotopy analysis method; k-fractional Riemann-Liouville derivative; Laplace transform.

DOI: 10.1504/IJDSDE.2017.086667

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.3, pp.240 - 258

Received: 24 Jun 2016
Accepted: 17 Dec 2016

Published online: 08 Sep 2017 *

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