Jackson Differential Operator Associated with Generalized Mittag–Leffler Function

Adel A. Attiya; Mansour F. Yassen; Abdelhamid Albaid

doi:10.3390/fractalfract7050362

Jackson Differential Operator Associated with Generalized Mittag–Leffler Function

Adel A. Attiya, Mansour F. Yassen, Abdelhamid Albaid

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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–Szegő problem. Some results that represent special cases of this family that have been studied before are also highlighted.

Original language	English
Article number	362
Journal	Fractal and Fractional
Volume	7
Issue number	5
DOIs	https://doi.org/10.3390/fractalfract7050362
State	Published - May 2023

Keywords

analytic functions
differential subordination
Fekete–Szegő function
Gaussian hypergeometric function
Jackson differential operator
Mittag–Leffler function
operators in geometric function theory
quantum calculus
subordination relation
univalent functions

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title = "Jackson Differential Operator Associated with Generalized Mittag–Leffler Function",

abstract = "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–Szeg{\H o} problem. Some results that represent special cases of this family that have been studied before are also highlighted.",

keywords = "analytic functions, differential subordination, Fekete–Szeg{\H o} function, Gaussian hypergeometric function, Jackson differential operator, Mittag–Leffler function, operators in geometric function theory, quantum calculus, subordination relation, univalent functions",

author = "Attiya, \{Adel A.\} and Yassen, \{Mansour F.\} and Abdelhamid Albaid",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

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language = "English",

volume = "7",

journal = "Fractal and Fractional",

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T1 - Jackson Differential Operator Associated with Generalized Mittag–Leffler Function

AU - Attiya, Adel A.

AU - Yassen, Mansour F.

AU - Albaid, Abdelhamid

PY - 2023/5

Y1 - 2023/5

N2 - 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–Szegő problem. Some results that represent special cases of this family that have been studied before are also highlighted.

AB - 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–Szegő problem. Some results that represent special cases of this family that have been studied before are also highlighted.

KW - analytic functions

KW - differential subordination

KW - Fekete–Szegő function

KW - Gaussian hypergeometric function

KW - Jackson differential operator

KW - Mittag–Leffler function

KW - operators in geometric function theory

KW - quantum calculus

KW - subordination relation

KW - univalent functions

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DO - 10.3390/fractalfract7050362

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AN - SCOPUS:85160327209

SN - 2504-3110

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 5

M1 - 362

ER -

Jackson Differential Operator Associated with Generalized Mittag–Leffler Function

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