A new theory of analytic functions has been recently introduced in the sense of conformable fractional derivative. In addition, the concept of fractional contour integral has also been developed. In this paper, we propose and prove some new results on complex fractional integration. First, we establish necessary and sufficient conditions for a continuous function to have antiderivative in the conformable sense. Finally, some of the well-known Cauchy´s integral theorems will also be the subject of the extension that we do in this paper.

中文翻译：

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关于复杂整合积分的新结果

最近在顺应分数导数的意义上引入了一种新的解析函数理论。此外，分数轮廓积分的概念也得到了发展。在本文中，我们提出并证明了有关复分数积分的一些新结果。首先，我们为连续函数建立了必要且充分的条件，使其具有顺应意义上的反导数。最后，一些著名的柯西积分定理也将成为本文扩展的主题。