Quantum–Fractal–Fractional Operator in a Complex Domain
In this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create an entirely novel subclass of analytical functions in the unit disk....
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/57 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589153257127936 |
|---|---|
| author | Adel A. Attiya Rabha W. Ibrahim Ali H. Hakami Nak Eun Cho Mansour F. Yassen |
| author_facet | Adel A. Attiya Rabha W. Ibrahim Ali H. Hakami Nak Eun Cho Mansour F. Yassen |
| author_sort | Adel A. Attiya |
| collection | DOAJ |
| description | In this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create an entirely novel subclass of analytical functions in the unit disk. Motivated by the concept of differential subordination, we explore the most important geometric properties of this novel operator. This leads to a study on a set of differential inequalities in the open unit disk. We focus on the conditions to obtain a bounded turning function of QFFOs. Some examples are considered, involving special functions like Bessel and generalized hypergeometric functions. |
| format | Article |
| id | doaj-art-efca356813cc483581a6a2162eca077e |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-efca356813cc483581a6a2162eca077e2025-01-24T13:22:17ZengMDPI AGAxioms2075-16802025-01-011415710.3390/axioms14010057Quantum–Fractal–Fractional Operator in a Complex DomainAdel A. Attiya0Rabha W. Ibrahim1Ali H. Hakami2Nak Eun Cho3Mansour F. Yassen4Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi ArabiaInformation and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar 64001, IraqDepartment of Mathematics, College of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi ArabiaDepartment of Applied Mathematics, Pukyong National University, Busan 48513, Republic of KoreaDepartment of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi ArabiaIn this effort, we extend the fractal–fractional operators into the complex plane together with the quantum calculus derivative to obtain a quantum–fractal–fractional operators (QFFOs). Using this newly created operator, we create an entirely novel subclass of analytical functions in the unit disk. Motivated by the concept of differential subordination, we explore the most important geometric properties of this novel operator. This leads to a study on a set of differential inequalities in the open unit disk. We focus on the conditions to obtain a bounded turning function of QFFOs. Some examples are considered, involving special functions like Bessel and generalized hypergeometric functions.https://www.mdpi.com/2075-1680/14/1/57fractal–fractional operatorfractional calculusquantum calculusanalytic functiondifferential subordinationunivalent function |
| spellingShingle | Adel A. Attiya Rabha W. Ibrahim Ali H. Hakami Nak Eun Cho Mansour F. Yassen Quantum–Fractal–Fractional Operator in a Complex Domain Axioms fractal–fractional operator fractional calculus quantum calculus analytic function differential subordination univalent function |
| title | Quantum–Fractal–Fractional Operator in a Complex Domain |
| title_full | Quantum–Fractal–Fractional Operator in a Complex Domain |
| title_fullStr | Quantum–Fractal–Fractional Operator in a Complex Domain |
| title_full_unstemmed | Quantum–Fractal–Fractional Operator in a Complex Domain |
| title_short | Quantum–Fractal–Fractional Operator in a Complex Domain |
| title_sort | quantum fractal fractional operator in a complex domain |
| topic | fractal–fractional operator fractional calculus quantum calculus analytic function differential subordination univalent function |
| url | https://www.mdpi.com/2075-1680/14/1/57 |
| work_keys_str_mv | AT adelaattiya quantumfractalfractionaloperatorinacomplexdomain AT rabhawibrahim quantumfractalfractionaloperatorinacomplexdomain AT alihhakami quantumfractalfractionaloperatorinacomplexdomain AT nakeuncho quantumfractalfractionaloperatorinacomplexdomain AT mansourfyassen quantumfractalfractionaloperatorinacomplexdomain |