In this paper, we discuss the relationship between the Zain Ul Abadin Zafar (ZZ) transform with Laplace and Aboodh transforms. Further, the ZZ transform is applied to the fractional derivative with the Mittag-Leffler kernel defined in both the Caputo and Riemann-Liouville sense. In order to illustrate the validity and applicability of the transform, we solve some illustrative examples.

中文翻译：

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用Mittag-Leffler内核将ZZ转换为分数运算符的新方面

在本文中，我们讨论了Zain Ul Abadin Zafar（ZZ）变换与Laplace变换和Aboodh变换之间的关系。此外，将ZZ变换应用于在Caputo和Riemann-Liouville意义上定义的Mittag-Leffler核的分数导数。为了说明该变换的有效性和适用性，我们解决一些说明性示例。