A Novel Approach for Korteweg-de Vries Equation of Fractional Order

Authors

  • Dumitru Baleanu Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Çankaya University, Balgat 0630, Ankara, Turkey | Institute of Space Sciences, Magurele-Bucharest, Romania
  • Hassan Kamil Jassim Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq
Abstract:

In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very effective and simple and can be applied for linear and nonlinear problems in mathematical physics.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation

Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle n...

full text

Lie Symmetry Analysis and Exact Solutions of General Time Fractional Fifth-order Korteweg-de Vries Equation

In this paper, using the Lie group analysis method, we study the invariance properties of the general time fractional fifth-order Korteweg-de Vries (KdV) equation. A systematic research to derive Lie point symmetries of the equation is performed. In the sense of point symmetry, all of the geometric vector fields and the symmetry reductions of the equation are obtained, the exact power series so...

full text

Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

A proper bilinear form is proposed for the N = 1 supersymmetric modified Korteweg-de Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it.

full text

Korteweg-de Vries Equation in Bounded Domains

where μ, ν are positive constants. This equation, in the case μ = 0, was derived independently by Sivashinsky [1] and Kuramoto [2] with the purpose to model amplitude and phase expansion of pattern formations in different physical situations, for example, in the theory of a flame propagation in turbulent flows of gaseous combustible mixtures, see Sivashinsky [1], and in the theory of turbulence...

full text

Forced oscillations of a damped‎ ‎Korteweg-de Vries equation on a periodic domain

‎In this paper‎, ‎we investigate a damped Korteweg-de‎ ‎Vries equation with forcing on a periodic domain‎ ‎$mathbb{T}=mathbb{R}/(2pimathbb{Z})$‎. ‎We can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

full text

The tanh method for solutions of the nonlinear modied Korteweg de Vries equation

In this paper, we have studied on the solutions of modied KdV equation andalso on the stability of them. We use the tanh method for this investigationand given solutions are good-behavior. The solution is shock wave and can beused in the physical investigations

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 5  issue 2

pages  192- 198

publication date 2019-04-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023