In this paper, we discuss the extended generalized multi-index Bessel function by using the extended beta type function. Then we investigate its several properties including integral representation, derivatives, beta transform, Laplace transform, Mellin transforms, and some relations of extension of extended generalized multi-index Bessel function (E¹GMBF) with the Laguerre polynomial and Whittaker functions. Further, we also discuss the composition of the generalized fractional integral operator having Appell function as a kernel with the extension of extended generalized multi-index Bessel function and establish these results in terms of Wright functions.

中文翻译：

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扩展的广义多索引Bessel函数的积分变换

在本文中，我们将使用扩展的beta类型函数来讨论扩展的广义多索引Bessel函数。然后，我们研究了它的几个属性，包括积分表示，导数，β变换，拉普拉斯变换，Mellin变换以及扩展的广义多索引Bessel函数（E ¹ GMBF）与Laguerre多项式和Whittaker函数的扩展的某些关系。此外，我们还讨论了具有Appell函数作为扩展扩展的广义多索引Bessel函数的核的广义分数积分算子的组成，并根据Wright函数建立了这些结果。