The aim of this study is to introduce new (presumed) generalized fractional integral operators involving -function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized -series and also to study the different properties of the generalized -series. The corresponding assertions in terms of Euler and Laplace transform methods are presented. Due to the general nature of the -function and the generalized -series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.

中文翻译：

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广义分数积分算子下广义M系列的某些性质

本研究的目的是引入新的（假定的）广义分数积分算子，将-函数作为内核。此外，两个定理已经被这些运营商，为了这个广义提供图像公式下开发的-系列，并研究推广的不同属性-系列。根据欧拉和拉普拉斯变换方法给出了相应的断言。由于-函数和广义-级数的一般性质，许多涉及特殊函数的结果只能通过为参数设置适当的值来实现。