Jackson Differential Operator Associated with Generalized Mittag-Leffler Function

Quantum calculus plays a significant role in many different branches such as quantum physics, hypergeometric series theory, and other physical phenomena. In our paper and using quantitative calculus, we introduce a new family of normalized analytic functions in the open unit disk, which relates to both the generalized Mittag-Leffler function and the Jackson differential operator. By using a differential subordination virtue, we obtain some important properties such as coefficient bounds and the Fekete-Szego problem. Some results that represent special cases of this family that have been studied before are also highlighted.