Electron. J. Diff. Equ., Vol. 2014 (2014), No. 66, pp. 1-12.

Solution of the KdV equation with fractional time derivative via variational method

Youwei Zhang

Abstract:
This article presents a formulation of the time-fractional generalized Korteweg-de Vries (KdV) equation using the Euler-Lagrange variational technique in the Riemann-Liouville derivative sense. It finds an approximate solitary wave solution, and shows that He's variational iteration method is an efficient technique in finding the solution.

Submitted November 5, 2013. Published March 7, 2014.
Math Subject Classifications: 35R11, 35G20.
Key Words: Riemann-Liouville fractional derivative; Euler-Lagrange equation; Riesz fractional derivative; generalized KdV equation; He's variational iteration method; solitary wave.

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Youwei Zhang
Department of Mathematics, Hexi University
Gansu 734000, China
email: ywzhang0288@163.com

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