The aim of this paper is to propose the Atangana–Baleanu fractional methodology for fathoming the Van der Pol damping model by using the reproducing kernel algorithm. To this end, we discuss the mathematical structure of this new approach and some other numerical properties of solutions. Furthermore, all needed requirements for characterizing solutions by applying the reproducing kernel algorithm are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate Atangana–Baleanu fractional solutions are proposed. Finally, numerical simulations in fractional emotion is constructed one next to the other with tabulated data and graphical portrayals.

中文翻译：

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考虑 ATANGANA-BALEANU 分数法的 Van DER POL 阻尼模型数值解的再现核算法

本文的目的是提出 Atangana-Baleanu 分数方法，用于通过使用再现核算法来了解 Van der Pol 阻尼模型。为此，我们讨论了这种新方法的数学结构以及解的其他一些数值性质。此外，对通过应用再现内核算法来表征解决方案的所有必要要求进行了辩论。在这个方向上，提出了解析和近似Atangana-Baleanu分数解的现代趋势和新的计算算法。最后，用表格数据和图形描绘一个接一个地构建分数情感的数值模拟。