On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method

Volume 9, Issue 9, pp 5463--5470 http://dx.doi.org/10.22436/jnsa.009.09.14

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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.

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Keywords

• Time-fractional KdV
• homotopy analysis Laplace transform method
• homotopy polynomial
• approximate solution
• optimal value.

MSC

•  47H10
•  54H25

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