Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G/G)-Expansion Method

被引：48

作者：

Khan, Hassan ^{[1
]}

Barak, Shoaib ^{[2
]}

Kumam, Poom ^{[3
,4
]}

Arif, Muhammad ^{[1
]}

机构：

[1] Abdul Wali Khan Univ, Dept Math, Mardan 23200, Pakistan

[2] Allama Iqbal Open Univ, Dept Math, Islamabad 44000, Pakistan

[3] KMUTT, Theoret & Computat Sci TaCS Ctr, Fac Sci, Dept Math, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[4] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 04期

关键词：

(G '/G)-expansion method; fractional Klein-Gordon equation; fractional Gas Dynamics equation; exact solutions; (G'/G)-EXPANSION METHOD; CALCULUS;

D O I：

10.3390/sym11040566

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 article, the (G/G)-expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie's operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in (G/G), where G=G() satisfies a second order linear ordinary differential equation. In this paper, (G/G)-expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions.

引用

页数：12

共 33 条

[1]

ABUTEEN E., 2016, J MATH STAT, V1, P23, DOI DOI 10.3844/JMSSP.2016.23.33

[2] A NEW NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS [J].