International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3242 2020 2020 Department of Mathematics College of Education Mustansiriyah University, Iraq Jaafer Jaafer Department of Mathematics, College of Computer Science and Mathematics, University of Thi-Qar, Iraq Ehsan M. Hameed Department of Applied Sciences, University of Technology, Iraq Jehad R. Kider In this paper, the basic properties of the convex fuzzy metric space will be presented. In particular, the proof of the fixed-point theorem for the fuzzy contraction single valued functions will be discussed. Furthermore, the solution system of linear equations, Volterra equations and Fredholm integral equations will be obtained as a direct application of the fixed-point theorem. 2025 2025 60 69 10.54216/IJNS.250306 https://www.americaspg.com/articleinfo/21/show/3242