In this paper, we have studied the time-fractional Zakharov-Kuznetsov equation (TFZKE) via natural transform decomposition method (NTDM) with nonsingular kernel derivatives. The fractional derivative considered in Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in Caputo sense (ABC). We employed natural transform (NT) on TFZKE followed by inverse natural transform, to obtain the solution of the equation. To validate the method, we have considered a few examples and compared with the actual results. Numerical results are in accordance with the existing results.

中文翻译：

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基于非奇异核导数的自然变换分解法求解时间分数阶Zakharov-Kuznetsov方程的数值解

在本文中，我们通过具有非奇异核导数的自然变换分解方法 (NTDM) 研究了时间分数的 Zakharov-Kuznetsov 方程 (TFZKE)。Caputo-Fabrizio (CF) 中考虑的分数导数和 Caputo 意义 (ABC) 中的 Atangana-Baleanu 导数。我们在 TFZKE 上采用自然变换 (NT)，然后进行逆自然变换，以获得方程的解。为了验证该方法，我们考虑了一些示例并与实际结果进行了比较。数值结果与现有结果一致。