Fractional Differential Operator Based on Quantum Calculus and Bi-Close-to-Convex Functions

Zeya Jia, Alina Alb Lupaş, Haifa Bin Jebreen, Georgia Irina Oros, Teodor Bulboacă () and Qazi Zahoor Ahmad ()
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Zeya Jia: School of Mathematics and Statistics, Zhumadian Academy of Industry Innovation and Development, Huanghuai University, Zhumadian 463000, China
Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Haifa Bin Jebreen: Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Qazi Zahoor Ahmad: Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan

Mathematics, 2024, vol. 12, issue 13, 1-19

Abstract: In this article, we first consider the fractional q -differential operator and the λ , q -fractional differintegral operator D q λ : A → A . Using the λ , q -fractional differintegral operator, we define two new subclasses of analytic functions: the subclass S * q , β , λ of starlike functions of order β and the class C Σ λ , q α of bi-close-to-convex functions of order β . We explore the results on coefficient inequality and Fekete–Szegö problems for functions belonging to the class S * q , β , λ . Using the Faber polynomial technique, we derive upper bounds for the nth coefficient of functions in the class of bi-close-to-convex functions of order β . We also investigate the erratic behavior of the initial coefficients in the class C Σ λ , q α of bi-close-to-convex functions. Furthermore, we address some known problems to demonstrate the connection between our new work and existing research.

Keywords: convex functions; starlike functions; close-to-convex functions; bi-close-to-convex functions; fractional q-differintegral operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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