Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

doi:10.1088/1674-1056/22/11/110202

中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/22/11/110202

Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

Ahmet Bekir^a, Özkan Güner^b

a Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey;
b Dumlupínar University, School of Applied Sciences, Department of Management Information Systems, Kutahya, Turkey

收稿日期:2013-03-04 修回日期:2013-04-04 出版日期:2013-09-28 发布日期:2013-09-28

Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

Ahmet Bekir^a, Özkan Güner^b

a Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey;
b Dumlupínar University, School of Applied Sciences, Department of Management Information Systems, Kutahya, Turkey

Received:2013-03-04 Revised:2013-04-04 Online:2013-09-28 Published:2013-09-28
Contact: Ahmet Bekir E-mail:abekir@ogu.edu.tr

摘要/Abstract

摘要： In this paper, we use the fractional complex transform and the (G’/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie’s modified Riemann–Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.

关键词: (G’/G)-expansion method, time-fractional Burgers equation, fractional-order biological population model, space–time fractional Whitham–Broer–Kaup equations

Abstract: In this paper, we use the fractional complex transform and the (G’/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie’s modified Riemann–Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.

Key words: (G’/G)-expansion method, time-fractional Burgers equation, fractional-order biological population model, space–time fractional Whitham–Broer–Kaup equations

中图分类号: (Partial differential equations)

02.30.Jr

02.70.Wz (Symbolic computation (computer algebra)) 05.45.Yv (Solitons) 94.05.Fg (Solitons and solitary waves)

Ahmet Bekir, Özkan Güner. Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method[J]. 中国物理B, 2013, 22(11): 110202-110202.

Ahmet Bekir, Özkan Güner. Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method[J]. Chin. Phys. B, 2013, 22(11): 110202-110202.

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Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

Exact solutions of nonlinear fractional differential equations by (G’/G)-expansion method

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