On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method
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Authors
Chong Li
- School of Mines, Key Laboratory of Deep Coal Resource Mining of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, China.
Amit Kumar
- Department of Mathematics, National Institute of Technology, Jamshedpur 831014, India.
Sunil Kumar
- Department of Mathematics, National Institute of Technology, Jamshedpur 831014, India.
Xiao-Jun Yang
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Abstract
The approximate solution of the time-fractional KdV equation (KdV) by using modified homotopy
analysis Laplace transform method, which is a combined form of the Laplace transform and homotopy
analysis methods, is investigated for the first time in this article. Comparison of series solutions between
under a rapid convergence and the optimal values of convergence parameter \(\hbar\) is made. The results through
the \(L_2\) and \(L_\infty\) error norms are also analyzed. The validity,
exibility, and accuracy of the proposed method
is conformed through the numerical computations as well as graphical presentations of the results.
Share and Cite
ISRP Style
Chong Li, Amit Kumar, Sunil Kumar, Xiao-Jun Yang, On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 9, 5463--5470
AMA Style
Li Chong, Kumar Amit, Kumar Sunil, Yang Xiao-Jun, On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method. J. Nonlinear Sci. Appl. (2016); 9(9):5463--5470
Chicago/Turabian Style
Li, Chong, Kumar, Amit, Kumar, Sunil, Yang, Xiao-Jun. "On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method." Journal of Nonlinear Sciences and Applications, 9, no. 9 (2016): 5463--5470
Keywords
- Time-fractional KdV
- homotopy analysis Laplace transform method
- homotopy polynomial
- approximate solution
- optimal value.
MSC
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