AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA025290127
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RESEARCH ARTICLE

New horizons in analytic function classes induced by the Erdélyi–Kober fractional integral operators

Stalin Thangamani1 ,  Dumitru Baleanu2 ,  Parthiban Lourdu1,3 ,  Majeed Ahmad Yousif4 ,  Pshtiwan Othman Mohammed5,6*
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1 Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, India
2 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3 Department of Mathematics, Agni College of Technology, Anna University, Chennai, India
4 Department of Mathematics, College of Education, University of Zakho, Duhok, Iraq
5 Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq
6 University Uninettuno, Corso Vittorio Emanuele II, Rome, Italy
IJOCTA, 025290127 https://doi.org/10.36922/IJOCTA025290127
Received: 19 July 2025 | Revised: 14 November 2025 | Accepted: 19 November 2025 | Published online: 9 December 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This study investigates a new subclass of analytic and univalent functions in the open unit disk, through the convolution of normalized analytic functions with a generalized Erdélyi–Kober fractional integral operator. The main objective is to define a new subclass TS(β, γ) related with the normalized form of the Erdélyi–Kober fractional integral operator Kϑδ and explore its geometrical properties. This study obtains sharp coefficient bounds and geometric characteristics such as growth, and distortion properties. Furthermore, convexity, close-to-convexity, radii of and starlikeness, extremal functions, and inclusion relations are determined. These results contribute to the broader understanding of defined subclass within geometric function theory and provide a mathematical foundation for modelling phenomena in fractional calculus, conformal mapping, and applied engineering contexts. The study also highlights limitations associated with the operator parameters and suggests extensions to numerical and control-based models for future investigation.

Graphical abstract
Keywords
Univalent functions
Subordination
Operator-defined function classes
Starlikeness and convexity
Funding
None.
Conflict of interest
Dumitru Baleanu is an Editorial Board Member of this journal, but was not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. Separately, other authors declared that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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