Work

On Two Broad Subfamilies of Liouville-Caputo-Type Fractional Derivatives Governed by Gregory Numbers

Year: 2026

Type: article

Abstract: In this paper, by employing Liouville--Caputo-type fractional derivatives and subordination to the generating function of the Gregory coefficients, we introduce two comprehensive subfamilies, denoted by $E_{\digamma}(\Psi_{u},\rho,$ $\daleth,$ $\gimel)$ and $C_{\digamma}(\Psi_{u},\phi)$, within the family of bi-univalent functions, and demonstrate that these subfamilies are non-empty. We establish estimates for the initial Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $, as well as for the Fekete--Szegö functional associated with functions belonging to these classes. The originality of the proofs and the resulting characterizations are expected to inspire further investigation into these analytic bi-univalent function subfamilies.

Source: International Journal of Analysis and Applications

DOI: 10.28924/2291-8639-24-2026-87

Authors: Feras Yousef, Tariq Al-Hawary, Jamal Salah, Basem Aref Frasin, Mohamed Illafe

Institutions: University of Jordan, Al-Balqa Applied University, A'Sharqiyah University, Al al-Bayt University, Navajo Technical University

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $450

OpenAlex ID: W7139123721

FWCI: 3.932

Cites: 17

Cited by: 2

Related to: 10