In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator and its inverse operator , involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed.

中文翻译：

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带有广义贝塞尔-马特兰函数的一些分数算子

在本文中，我们旨在确定分数演算领域中广义Bessel-Maitland函数的一些结果。在此，考虑了广义的Bessel-Maitland函数和Mittag-Leffler函数的一些关系。我们通过使用广义的Bessel-Maitland函数来开发Saigo和Riemann-Liouville分数阶积分算子，结果可以以Fox-Wright函数的形式看到。我们建立一个新的算子及其逆算子，以广义的Bessel-Maitland函数为核，并讨论其收敛性和有界性。此外，还开发了Riemann-Liouville运算符和新运算符的积分变换（Laplace）。