New results on complex conformable integral

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 establ...

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Bibliographic Details
Published in:	AIMS mathematics Vol. 5; no. 6; pp. 7695 - 7710
Main Authors:	Martínez, Francisco, Martínez, Inmaculada, K. A. Kaabar, Mohammed, Paredes, Silvestre
Format:	Journal Article
Language:	English
Published:	AIMS Press 01-01-2020
Subjects:	cauchy’s integral theorem conformable fractional derivative conformable fractional integral fractional analytic functions fractional contour integrals
Online Access:	Get full text
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Summary:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2020492