SOLVING SOME IMPORTANT NONLINEAR TIME-FRACTIONAL EVOLUTION EQUATIONS BY USING THE (G′/G)-EXPANSION METHOD

被引：2

作者：

Djilali, Medjahed ^{[1
,2
]}

Hakem, Ali ^{[2
]}

机构：

[1] Oran Higher Sch Econ, Oran 31000, Algeria

[2] Univ Djillali Liabes Sidi Bel Abbes, Lab ACEDP, Sidi Bel Abbes 22000, Algeria

来源：

JOURNAL OF SCIENCE AND ARTS | 2020年 / 04期

关键词：

Burgers-Fisher equation; Kaup-Kupershmidt equation; time-fractional; Shallow Water Wave equation; traveling wave solutions; BURGERS-FISHER EQUATION; KAUP-KUPERSHMIDT-EQUATION; TRAVELING-WAVE SOLUTIONS; SOLITON-SOLUTIONS; SYMMETRIES; FORMS; 5TH-ORDER;

D O I：

10.46939/J.Sci.Arts-20.4-a04

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：

The aim of the present study is to find the exact solutions for three gen-eralized nonlinear time-fractional evolution equations, Kaup-Kupershmidt equation, BurgersFisher equation and, Shallow Water Wave equation. By using the (G'/G)-expansion method and depending on second order linear ODE as well as the complex transformation, three kinds of solutions (hyperbolic, trigonometric, and rational) are obtained. With the help of Mathematica software package, difficult algebraic systems are solved and surfaces of some particular solutions of the equations under study are plotted.

引用

页码：815 / 832

页数：18

共 50 条

[31] The G′G-expansion Method for Solving Nonlinear Klein-Gordon Equations
Zayedand, E. M. E.
El-Malky, M. A. S.
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
[32] The new approach of the generalized (G '/G)expansion method for nonlinear evolution equations
Alam, Md Nur
Akbar, M. Ali
AIN SHAMS ENGINEERING JOURNAL, 2014, 5 (02) : 595 - 603
[33] Analytical solutions with the improved (G'/G)-expansion method for nonlinear evolution equations
Kaplan, Melike
Bekir, Ahmet
Akbulut, Arzu
INTERNATIONAL CONFERENCE ON QUANTUM SCIENCE AND APPLICATIONS (ICQSA-2016), 2016, 766
[34] A generalized (G′/G)-expansion method and its applications to nonlinear evolution equations
Lue, Hai-Ling
Liu, Xi-Qiang
Niu, Lei
APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (11) : 3811 - 3816
[35] Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the exp(-φ/(ε))-expansion method
Hosseini, K.
Bekir, A.
Ansari, R.
OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (04)
[36] (G′/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics
Zheng Bin
COMMUNICATIONS IN THEORETICAL PHYSICS, 2012, 58 (05) : 623 - 630
[37] (G′/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics
郑滨
CommunicationsinTheoreticalPhysics, 2012, 58 (11) : 623 - 630
[38] Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G)-expansion method
Islam, Tarikul
Akbar, M. Ali
Azad, Abul Kalam
JOURNAL OF OCEAN ENGINEERING AND SCIENCE, 2018, 3 (01) : 76 - 81
[39] The two variable (φ′/φ, 1/φ)-expansion method for solving the time-fractional partial differential equations
Zhao, Yunmei
He, Yinghui
Yang, Huizhang
AIMS MATHEMATICS, 2020, 5 (05): : 4121 - 4135
[40] A stochastic method for solving time-fractional differential equations
Guidotti, Nicolas L.
Acebron, Juan A.
Monteiro, Jose
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 159 : 240 - 253

← 1 2 3 4 5 →