论文标题
进一步研究符合符合的分数高几何函数
Further study on the conformable fractional Gauss hypergeometric function
论文作者
论文摘要
本文介绍了一项详尽的研究，该研究对符合的分数高几何函数（CFGHF）提出了一些详尽的研究。我们首先求解有关分数常规点$ x = 1 $和$ x = \ infty $的符合符合的分数高几何方程（CFGHE）。接下来，建立了CFGHF的各种生成功能。我们还为CFGHF开发了一些差异形式。随后，报告了差分运算符和连续关系。此外，我们介绍了CFGHF的符合符合的分数积分表示和分数拉普拉斯变换。作为一种应用，在对自变量进行了适当更改后，我们提供了一些已知符合的分数微分方程的通用解决方案，这些方程可以通过CFGHF编写。
This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) 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 the 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.
