Certain fractional integral with generalized Mittag-Leffler-type function of arbitrary order

In this paper, we define a fractional integral operator involving the generalized Mittag-Leffler function in the kernel. We establish the boundedness and composition properties of this new operator. The Laplace and Mellin transforms of this operator are obtained. Applying the Laplace transform, we solve certain fractional differential equations. Additionally, some special cases of the established results are presented.