Explicit Jacobi elliptic exact solutions for nonlinear partial fractional differential equations

被引：0
作者：
Khaled A Gepreel
机构：
[1] Zagazig University,Mathematics Department, Faculty of Science
[2] Taif University,Mathematics Department, Faculty of Science
来源：
Advances in Difference Equations | / 2014卷
关键词：
fractional calculus; fractional complex transformation; modified Riemann-Liouville derivative; Jacobi elliptic functions; nonlinear fractional differential equations;
D O I：
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摘要：
In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. An algebraic method is improved to construct uniformly a series of exact solutions for some nonlinear time-space fractional partial differential equations. We construct successfully a series of some exact solutions including the elliptic doubly periodic solutions with the aid of computerized symbolic computation software package such as Maple or Mathematica. This method is efficient and powerful in solving a wide classes of nonlinear partial fractional differential equations. The Jacobi elliptic doubly periodic solutions are generated by the trigonometric exact solutions and the hyperbolic exact solutions when the modulus m→0 and m→1, respectively.
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