International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4008 2020 2020 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan Isra Isra Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates Wael Mahmoud Mohammad Salameh Department of Mathematics, Al-Albayt University, Mafraq 25113, Jordan Saleem Ashhab Gitam Institute of Science, GITAM University, Visakhapatnam 530045, India Biswajit Rath Basic and Applied Scientifc Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam,Saudi Arabia Eada Ahmed Al Al-Zahrani This study investigates the second-order Hankel determinant in the context of certain analytic functions to find upper bounds, incorporating neutrosophic logic to handle uncertainty in coefficient estimation. The normalized conditions ג)0)=0 ג′(0) = 1 are analyzed through both classical and neutrosophic frameworks. We derive: • Sharp neutrosophic bounds for |H2,2,ϖ| when ϖ ∈ (1, 32] • Optimal bounds for |H2,3| at ϖ = 32 in G(ϖ) and Q(ϖ) • Neutrosophic logarithmic coefficient determinants with τ -ι-φ membership degrees The framework demonstrates robustness when coefficients exhibit simultaneous membershipnon-membership characteristics. 2026 2026 110 122 10.54216/IJNS.270210 https://www.americaspg.com/articleinfo/21/show/4008