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Time-fractional Drinfeld-Sokolov-Wilson system: Lie symmetry analysis, analytical solutions and conservation laws

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Abstract.

In this paper, under the background of the Riemann-Liouville fractional differential, the Lie point symmetries are obtained by using the Lie symmetry method. The symmetry reductions are also derived ulteriorly. Next, the power series solution and its convergence proof are given. Finally, conservation laws are well constructed based on the Noether theorem. Especially, the approximate analytical solution is studied by employing the q-homotopy analysis method under the background of Caputo fractional differential. What is more, the dynamic behaviour of all these exact solutions of the equation are described with changing the value of \( \alpha\) .

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, Jiangsu, China

    Wenhao Liu & Yufeng Zhang

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  1. Wenhao Liu
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  2. Yufeng Zhang
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Correspondence to Yufeng Zhang.

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Liu, W., Zhang, Y. Time-fractional Drinfeld-Sokolov-Wilson system: Lie symmetry analysis, analytical solutions and conservation laws. Eur. Phys. J. Plus 134, 126 (2019). https://doi.org/10.1140/epjp/i2019-12490-8

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