International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3550 2020 2020 Branch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, Iraq Jaafer Jaafer Department of Mathematics College of Education Mustansiriyah University, Iraq Jaafer Hmood Eidi General Directorate of Curricula. Moe. Iraq Hussein S. ALallak This paper introduces a new class of mappings termed (α̂,β̂)−Ω-contraction mapping (briefly, "(α̂,β̂)−Ω−CMap") and establishes certain fixed-point (FP) results in the framework of Algebra fuzzy metric space. Additionally, we expanded our results to include the existence of a nonlinear integral equation solution. Results from this study improve, expand and generalization certain previously published results in the literature. 2025 2025 399 407 10.54216/IJNS.250433 https://www.americaspg.com/articleinfo/21/show/3550