In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

中文翻译：

---

具有非奇异核算子的时间分数阶耦合Burgers方程的分析

在本文中，我们通过具有非奇异核导数的自然分解方法研究了分数阶 Burgers 方程。Caputo-Fabrizio 和 Atangana-Baleanu 导数的文章中使用了两种分数导数。我们对分数阶 Burgers 方程采用自然变换，然后进行逆自然变换，得到方程的结果。为了验证该方法，我们考虑了两个示例并与确切结果进行了比较。