aspg-21-3314-1791472348 20261008151228 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Abdulmtalb Hussen School of Engineering, Math, & Technology, Navajo Technical University,Crownpoint, NM 87313, USA Mohamed Illafe School of Engineering, Math, & Technology, Navajo Technical University,Crownpoint, NM 87313, USA Abdelbaset Zeyani Mathematics and Statistics, Witchita State University, Witchita, KS, USA 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 417 434 3314 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250336 https://www.americaspg.com/journal/21/article/3314 https://www.americaspg.com/storage/81731768394.pdf