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AIMS Mathematics

2021, Volume 6, Issue 9: 10130-10163. doi: 10.3934/math.2021588
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Further study on the conformable fractional Gauss hypergeometric function

  • 1.
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • 2.
    Academy of Scientific Research and Technology (ASRT), Cairo, Egypt
  • 3.
    Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia
  • Received: 21 May 2021 Accepted: 09 July 2021 Published: 09 July 2021

  • MSC : 26A33, 33C05, 33C90, 34K37

  • This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points $ x = 1 $ and $ x = \infty $. Next, various generating functions of the CFGHF are established. We also develop some differential forms for the CFGHF. Subsequently, differential operators and contiguous relations are reported. Furthermore, we introduce the conformable fractional integral representation and the fractional Laplace transform of CFGHF. As an application, and after making a suitable change of the independent variable, we provide general solutions of some known conformable fractional differential equations, which could be written by means of the CFGHF.

    Citation: Mahmoud Abul-Ez, Mohra Zayed, Ali Youssef. Further study on the conformable fractional Gauss hypergeometric function[J]. AIMS Mathematics, 2021, 6(9): 10130-10163. doi: 10.3934/math.2021588

    Related Papers:

  • This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points $ x = 1 $ and $ x = \infty $. Next, various generating functions of the CFGHF are established. We also develop some differential forms for the CFGHF. Subsequently, differential operators and contiguous relations are reported. Furthermore, we introduce the conformable fractional integral representation and the fractional Laplace transform of CFGHF. As an application, and after making a suitable change of the independent variable, we provide general solutions of some known conformable fractional differential equations, which could be written by means of the CFGHF.


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