Certain Quantum Operator Related to Generalized Mittag–Leffler Function

In this paper, we present a novel class of analytic functions in the form (Formula presented.) in the unit disk. These functions establish a connection between the extended Mittag–Leffler function and the quantum operator presented in this paper, which is denoted by (Formula presented.) and is also an extension of the Raina function that combines with the Jackson derivative. Through the application of differential subordination methods, essential properties like bounds of coefficients and the Fekete–Szegő problem for this class are derived. Additionally, some results of special cases to this study that were previously studied were also highlighted.