Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation

doi:10.1088/1674-1056/22/1/010201

Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 10201-010201.doi: 10.1088/1674-1056/22/1/010201

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Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation

Khaled A. Gepreel^{a b}, Mohamed S. Mohamed^{b c}

a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt;
b Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia;
c Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

收稿日期:2012-05-29 修回日期:2012-06-26 出版日期:2012-12-01 发布日期:2012-12-01

Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation

Khaled A. Gepreel^{a b}, Mohamed S. Mohamed^{b c}

a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt;
b Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia;
c Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt

Received:2012-05-29 Revised:2012-06-26 Online:2012-12-01 Published:2012-12-01
Contact: Khaled A. Gepreel E-mail:kagepreel@yahoo.com

摘要/Abstract

摘要： The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives Klein-Gordon equation. This method introduces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

关键词: homotopy analysis method, nonlinear space-time fractional Klein-Gordon equation, Caputo derivative

Abstract: The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives Klein-Gordon equation. This method introduces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

Key words: homotopy analysis method, nonlinear space-time fractional Klein-Gordon equation, Caputo derivative

中图分类号: (Partial differential equations)

02.30.Jr

Khaled A. Gepreel, Mohamed S. Mohamed. Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation[J]. Chin. Phys. B, 2013, 22(1): 10201-010201.

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Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation

Analytical approximate solution for nonlinear space-time fractional Klein–Gordon equation

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