<p>In this paper, we develop a generating function framework associated with fractional operators involving Mittag-Leffler kernels. The proposed function arises from the series representation of a two-parameter Mittag-Leffler fractional derivative and provides a unified way to represent and analyze such nonlocal operators. We study the main analytical properties of the generating function, including its domain of convergence, growth behavior, and asymptotic properties. In addition, we derive integral representations and show a connection with the Laplace transform, which leads to an operator-based formulation and supports inversion procedures in the considered fractional framework. The results give a systematic approach for studying fractional operators with Mittag-Leffler kernels and help to clarify their structural properties.</p>