Exp-Function Method for Solving Fractional Partial Differential Equations

被引：101
作者：
Zheng, Bin [1 ]
机构：
[1] Shandong Univ Technol, Sch Sci, Zibo, Shandong 255049, Peoples R China
来源：
SCIENTIFIC WORLD JOURNAL | 2013年
关键词：
NONLINEAR EVOLUTION-EQUATIONS; RATIONAL EXPANSION METHOD; TRAVELING-WAVE SOLUTIONS; PERTURBATION TECHNIQUE; SYMBOLIC COMPUTATION; PERIODIC-SOLUTIONS; RICCATI EQUATION; (G'/G)-EXPANSION; ORDER;
D O I：
10.1155/2013/465723
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：
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space- time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.
引用
收藏
页数：8
相关论文
共 27 条
[1]   Compact finite difference method for the fractional diffusion equation [J].
Cui, Mingrong .
JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (20) :7792-7804
[2]   The Adomian decomposition method for solving partial differential equations of fractal order in finite domains [J].
El-Sayed, A. M. A. ;
Gaber, M. .
PHYSICS LETTERS A, 2006, 359 (03) :175-182
[3]   Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation [J].
El-Sayed, A. M. A. ;
Behiry, S. H. ;
Raslan, W. E. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (05) :1759-1765
[4]   The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics [J].
Guo, Shimin ;
Mei, Liquan ;
Li, Ying ;
Sun, Youfa .
PHYSICS LETTERS A, 2012, 376 (04) :407-411
[5]   The fractional variational iteration method using He's polynomials [J].
Guo, Shimin ;
Mei, Liquan .
PHYSICS LETTERS A, 2011, 375 (03) :309-313
[6]  
He J., 1997, COMMUN NONLINEAR SCI, V2, P230, DOI [DOI 10.1016/S1007-5704(97)90007-1, 10.1016/S1007-5704(97)90007-1]
[7]   A coupling method of a homotopy technique and a perturbation technique for non-linear problems [J].
He, JH .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2000, 35 (01) :37-43
[8]   Homotopy perturbation technique [J].
He, JH .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 178 (3-4) :257-262
[9]   Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method [J].
He, Ji-Huan ;
Zhang, Li-Na .
PHYSICS LETTERS A, 2008, 372 (07) :1044-1047
[10]   New periodic solutions for nonlinear evolution equations using Exp-function method [J].
He, Ji-Huan ;
Abdou, M. A. .
CHAOS SOLITONS & FRACTALS, 2007, 34 (05) :1421-1429
123