Certain families of admissible functions defined via fuzzy differential subordination and a generalized Mittag-Leffler function

Dalal Alhwikem; Abbas Kareem Wanas; Bedaa Alawi Abd; Ala Amourah; Sheza M. El-Deeb; Dalal Alhwikem; Abbas Kareem Wanas; Bedaa Alawi Abd; Ala Amourah; Sheza M. El-Deeb

doi:10.3934/math.2026041

AIMS Mathematics

2026, Volume 11, Issue 1: 943-956. doi: 10.3934/math.2026041

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Research article

Certain families of admissible functions defined via fuzzy differential subordination and a generalized Mittag-Leffler function

1.
Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
2.
Department of Mathematics, College of Education for Women, University of Al-Qadisiyah, Al Diwaniyah 58001, Al-Qadisiyah, Iraq
3.
Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
4.
Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman
5.
Jadara University Research Center, Jadara University, Jordan
6.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt; s.eldeeb@qu.edu.sa

Received: 05 December 2025 Revised: 03 January 2026 Accepted: 06 January 2026 Published: 13 January 2026
MSC : 30C20, 30C45, 30A20

In the present paper, we employ the generalized Mittag-Leffler function to investigate several fuzzy differential subordination results associated with suitable families of admissible functions in the open unit disk. By utilizing a refined analytic framework, we derive new inclusion relationships and establish sufficient conditions for fuzzy subordinating functions defined via Mittag-Leffler-type operators. Furthermore, the obtained results unify and extend a number of earlier findings in the theory of fuzzy analytic functions. These developments provide a deeper insight into the interaction between generalized special functions and the structure of fuzzy differential subordinations, offering potential applications to broader subclasses of analytic and bi-univalent functions, as well as to various operator-defined families in geometric function theory.
- fuzzy set,
- fuzzy differential subordination,
- fuzzy best dominant,
- analytic functions,
- convolution,
- admissible functions
Citation: Dalal Alhwikem, Abbas Kareem Wanas, Bedaa Alawi Abd, Ala Amourah, Sheza M. El-Deeb. Certain families of admissible functions defined via fuzzy differential subordination and a generalized Mittag-Leffler function[J]. AIMS Mathematics, 2026, 11(1): 943-956. doi: 10.3934/math.2026041

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Abstract

In the present paper, we employ the generalized Mittag-Leffler function to investigate several fuzzy differential subordination results associated with suitable families of admissible functions in the open unit disk. By utilizing a refined analytic framework, we derive new inclusion relationships and establish sufficient conditions for fuzzy subordinating functions defined via Mittag-Leffler-type operators. Furthermore, the obtained results unify and extend a number of earlier findings in the theory of fuzzy analytic functions. These developments provide a deeper insight into the interaction between generalized special functions and the structure of fuzzy differential subordinations, offering potential applications to broader subclasses of analytic and bi-univalent functions, as well as to various operator-defined families in geometric function theory.

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