Generalized KdV equation involving Riesz time-fractional derivatives: constructing and solution utilizing variational methods

被引：5

作者：

Alshenawy, R. ^{[1
,2
]}

Al-alwan, Ali ^{[1
]}

Elmandouh, A. A. ^{[1
,3
]}

机构：

[1] King Faisal Univ, Coll Sci, Dept Math & Stat, POB 400, Al Hasa 31982, Saudi Arabia

[2] Mansoura Univ, Fac Commerce, Dept Appl Stat & Insurance, Mansoura 35516, Egypt

[3] Mansoura Univ, Fac Sci, Dept Math, Mansoura, Egypt

来源：

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2020年 / 14卷 / 01期

关键词：

Solitary waves; Riemann-Liouville fractional derivative; Riesz fractional derivative; KdV equation; the method of He's variational iteration; PARTIAL-DIFFERENTIAL-EQUATIONS; ITERATION METHOD; ADOMIAN DECOMPOSITION; CONSERVATION-LAWS; ORDER; PRINCIPLES; CALCULUS; SPACE; FORMULATION; EXISTENCE;

D O I：

10.1080/16583655.2020.1737357

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this work, the time-fractional generalized Korteweg de Vries (TFGKdV) is derived by utilizing the method of a semi-inverse and the variational principles. Based on the initial condition relying on the dispersion and nonlinear coefficients, we can apply the He's variational iteration to construct an approximated solution for the TFGKdV equation. Finally, we study the impact of the fractional derivatives on the propagation and the structure of the solitary waves obtained from the solution of TFGKdV equation.

引用

页码：314 / 321

页数：8

共 61 条

[31] A generalized variational principle in micromorphic thermoelasticity [J].

He, JH .

MECHANICS RESEARCH COMMUNICATIONS, 2005, 32 (01) :93-98

[32] Variational principles for some nonlinear partial differential equations with variable coefficients [J].

He, JH .

CHAOS SOLITONS & FRACTALS, 2004, 19 (04) :847-851

[33]

He JH, 1997, INT J TURBO JET ENG, V14, P23

[34] Variational iteration method - Some recent results and new interpretations [J].

He, Ji-Huan .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 207 (01) :3-17

[35]

Inokuti M., 1978, Variational method in the mechanics of solids, V33, P156

[36] Extracting new solitary wave solutions of Benny-Luke equation and Phi-4 equation of fractional order by using (G'/G)-expansion method [J].

Khan, Umar ;

Ellahi, Rahmat ;

Khan, Rahmatullah ;

Mohyud-Din, Syed Tauseef .

OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (11)

[37] Invariant variational principles and conservation laws for some nonlinear partial differential equations with variable coefficients part II [J].

Khater, AH ;

Moussa, MHM ;

Abdul-Aziz, SF .

CHAOS SOLITONS & FRACTALS, 2003, 15 (01) :1-13

[38]

Kilbas A. A., 2006, THEORY APPL FRACTION, DOI 10.1016/S0304-0208(06)80001-0

[39]

Korteweg D.J., 1895, PHILOS MAG 5, V39, P422, DOI [10.1080/14786449508620739, DOI 10.1080/14786449508620739, 10.1080/14786435.2010.547337, DOI 10.1080/14786435.2010.547337]

[40] THE EXACT SOLUTION OF CERTAIN DIFFERENTIAL-EQUATIONS OF FRACTIONAL ORDER BY USING OPERATIONAL CALCULUS [J].

LUCHKO, YF ;

SRIVASTAVA, HM .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1995, 29 (08) :73-85

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