Research article

New results on complex conformable integral

  • Received: 07 August 2020 Accepted: 09 September 2020 Published: 27 September 2020
  • MSC : 26A33, 30Axx

  • 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.

    Citation: Francisco Martínez, Inmaculada Martínez, Mohammed K. A. Kaabar, Silvestre Paredes. New results on complex conformable integral[J]. AIMS Mathematics, 2020, 5(6): 7695-7710. doi: 10.3934/math.2020492

    Related Papers:

  • 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.



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