NDLI: Time-fractional KdV equation: formulation and solution using variational methods

Content Provider	Springer Nature Link
Author	El Wakil, S. A. Abulwafa, E. M. Zahran, M. A. Mahmoud, A. A.
Copyright Year	2010
Abstract	In this work, the semi-inverse method has been used to derive the Lagrangian of the Korteweg–de Vries (KdV) equation. Then the time operator of the Lagrangian of the KdV equation has been transformed into fractional domain in terms of the left-Riemann–Liouville fractional differential operator. The variational of the functional of this Lagrangian leads neatly to Euler–Lagrange equation. Via Agrawal’s method, one can easily derive the time-fractional KdV equation from this Euler–Lagrange equation. Remarkably, the time-fractional term in the resulting KdV equation is obtained in Riesz fractional derivative in a direct manner. As a second step, the derived time-fractional KdV equation is solved using He’s variational-iteration method. The calculations are carried out using initial condition depends on the nonlinear and dispersion coefficients of the KdV equation. We remark that more pronounced effects and deeper insight into the formation and properties of the resulting solitary wave by additionally considering the fractional order derivative beside the nonlinearity and dispersion terms.
Starting Page	55
Ending Page	63
Page Count	9
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	65
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-10-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Riemann–Liouville fractional differential operator Euler–Lagrange equation Riesz fractional derivative Fractional KdV equation He’s variational-iteration method Solitary wave Mechanical Engineering Automotive Engineering Vibration, Dynamical Systems, Control Mechanics
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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