Certain Subclasses of Bi-Univalent Functions Involving Caputo Fractional Derivatives with Bounded Boundary Rotation

Abbas Kareem Wanas (), Mohammad El-Ityan, Adel Salim Tayyah and Adriana Catas ()
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Abbas Kareem Wanas: Department of Mathematics, College of Education for Women, University of Al-Qadisiyah, Al Diwaniyah 58001, Iraq
Mohammad El-Ityan: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan
Adel Salim Tayyah: Department of Cybersecurity, College of Computer Science and Information Technology, University of Al-Qadisiyah, Al Diwaniyah 58002, Iraq
Adriana Catas: Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania

Mathematics, 2025, vol. 13, issue 21, 1-15

Abstract: In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator C ȷ ϱ , which encompasses and extends classical operators such as the Salagean differential operator and the Libera–Bernardi integral operator, we establish sharp coefficient estimates for the initial Taylor Maclaurin coefficients of functions within these subclasses. Furthermore, we derive Fekete–Szegö-type inequalities that provide bounds on the second and third coefficients and their linear combinations involving a real parameter. Our approach leverages subordination principles through analytic functions associated with the classes T ς ( ξ ) and R Ω ȷ , ϱ ( ϑ , ς , ξ ) , allowing a unified treatment of fractional differential operators in geometric function theory. The results generalize several known cases and open avenues for further exploration in fractional calculus applied to analytic function theory.

Keywords: bi-univalent functions; Caputo fractional derivatives; Fekete–Szegö inequalities; fractional differential operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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