In this paper, the exact traveling and solitary wave solutions of the fractional nonlinear Drinfeld–Sokolov–Wilson (DSW) system are obtained by employing the modified Khater (mK) method through a new fractional derivative. This system describes the flow of shallow water. Moreover, the stability property of the obtained solutions is also investigated by using the characteristics of the Hamiltonian system. Some plots are given to show more physical properties of the suggested model. The advantage and accuracy of the applied analytical schemes are verified and explained by using Mathematica 11.3, and then a comparison between our solutions and those obtained in previous research papers with different systematic schemes is carried out.
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Yue et al. (2020) studied this question.
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