COMPLEX MATHEMATICAL MODELING FOR ADVANCED FRACTAL–FRACTIONAL DIFFERENTIAL OPERATORS WITHIN SYMMETRY

Rabha W. Ibrahim, Suzan J. Obaiys, Yeliz Karaca () and Aydin Secer ()
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Rabha W. Ibrahim: Department of Computer Science and Mathematics, Lebanese American University, 13-5053 Beirut, Lebanon†Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC
Suzan J. Obaiys: ��Department of Computer System & Technology, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia
Yeliz Karaca: �University of Massachusetts (UMASS), Chan Medical School, 55 Lake Avenue North, Worcester, MA 01655, USA
Aydin Secer: �Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Biruni University, 34010 Zeytinburnu, Istanbul, Türkiye

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-17

Abstract: Non-local operators of differentiation are bestowed with capabilities of encompassing complex natural into mathematical equations. Symmetry as invariance under a specified group of transformations can allow for the concept to be applied extensively not only to spatial figures but also to abstract objects like mathematical expressions which can be said to be expressions of physical relevance, in particular dynamical equations. Derived from this point of view, it can be noted that the more complex physical problems are, the more complex mathematical operators of differentiation are required. Accordingly, the fractal–fractional operators (FFOs) are expanded into the complex plane in our research which revolves around a unique class of normalized analytic functions in the open unit disk. To bring FFOs (differential and integral) into the normalized class, the study aims to expand and modify them along with the investigation of the FFOs geometrically. The qualities of convexity and starlikeness are implicated in this study where the differential subordination technique serves as the foundation for the inquiry under consideration. Furthermore, a collection of differential FFO inequalities is taken into account, demonstrating that the normalized Fox–Wright function can contain all FFOs. Besides these steps, the concept of Grunsky factors is applied to investigate symmetry, while boundary value issues involving FFOs are probed. Consequently, the related properties and applications can be further developed, which requires the devotion to differential fractional problems and diverse complex problems in relation to viable applications, pointing out the room to modify and upgrade the existing methods for more optimal outcomes in challenging real-world problems.

Keywords: Univalent Function; Fractal Calculus; Fractional Calculus; Fractal–Fractional Operators; Open Unit Disk; Analytic Function; Subordination and Superordination; Grunsky Factors; Fox–Wright Function; Univalent Function; Boundary Value Problem; Symmetry; Symmetric Sense; Starlike Behavior; Fractional Differential Inequalities; Complex and Non-Differentiable Phenomena (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401941

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