Jackson Differential Operator Associated with Generalized Mittag-Leffler Function

Adel A. Attiya

doi:10.3390/fractalfract7050362

Jackson Differential Operator Associated with Generalized Mittag-Leffler Function

2023-04-28

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DOI：10.3390/fractalfract7050362

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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.

Keywords:

Mittag-Leffler function

Jackson differential operator

quantum calculus

analytic functions

univalent functions

subordination relation

differential subordination

operators in geometric function theory

Fekete-Szego function

Gaussian hypergeometric function

Jackson Differential Operator Associated with Generalized Mittag-Leffler Function

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