International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3314 2020 2020 School of Engineering, Math, & Technology, Navajo Technical University,Crownpoint, NM 87313, USA Abdulmtalb Abdulmtalb School of Engineering, Math, & Technology, Navajo Technical University,Crownpoint, NM 87313, USA Mohamed Illafe Mathematics and Statistics, Witchita State University, Witchita, KS, USA Abdelbaset Zeyani In this paper, a new subclass of bi-univalent functions linked to Lucas-Balancing polynomials is introduced. Bounds for the coefficients in the Taylor-Maclaurin series, denoted as |a2| and |a3|, are determined for these functions. The Fekete-Szeg¨o functional problems are also addressed, and bounds for the second Hankel determinant for functions in this specific subclass are established. Additionally, it is shown that by adjusting the parameters in the main findings, several new results can be derived. 2025 2025 417 434 10.54216/IJNS.250336 https://www.americaspg.com/articleinfo/21/show/3314