In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.

中文翻译：

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描述长表面波传播的分数 Oskolkov-Benjamin-Bona-Mahony-Burgers 方程解的数值和解析研究

在本文中，提出了一种求解时间分数 Oskolkov-Benjamin-Bona-Mahony-Burgers 型方程的新型无网格数值方案。所提出的数值方案是基于有限差分和堪萨径向基函数搭配方法。首先，使用有限差分格式对时间分数导数进行离散化，然后使用 Kansa 方法对空间导数进行离散化。本文还阐述了时间离散数值格式的稳定性和收敛性分析。此外，Kudryashov 方法已被用于获取孤子解，以便与数值结果进行比较。最后，进行数值模拟以确认所提出方案的适用性和准确性。