This paper aimed at obtaining the traveling-wave solution of the nonlinear time fractional regularized long-wave equation. In this approach, firstly, the time fractional derivative is accomplished using a finite difference with convergence order $ \mathcal{O}(\delta t^{2-\alpha}) $ for $ 0 < \alpha< 1 $ and the nonlinear term is linearized by a linearization technique. Then, the spatial terms are approximated with the help of the radial basis function (RBF). Numerical stability of the method is analyzed by applying the Von-Neumann linear stability analysis. Three invariant quantities corresponding to mass, momentum and energy are evaluated for further validation. Numerical results demonstrate the accuracy and validity of the proposed method.

中文翻译：

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离子声等离子体波中非线性分数正则化长波模型的数值模拟

本文旨在求得非线性时间分数阶正则化长波方程的行波解。在这种方法中，首先，时间分数阶导数是使用收敛阶数 $ \mathcal{O}(\delta t^{2-\alpha}) $ for $ 0 < \alpha< 1 $ 和非线性项通过线性化技术线性化。然后，在径向基函数 (RBF) 的帮助下近似空间项。通过应用冯诺依曼线性稳定性分析来分析该方法的数值稳定性。评估对应于质量、动量和能量的三个不变量以进行进一步验证。数值结果证明了所提出方法的准确性和有效性。