aspg-21-1276-1791472310 20261008151150 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2022 19 1 S. Obaid Jameel University of Wasit, College of Education for Pure Sciences, Mathematics department, Wasit, Iraq A. Mahdi Salih Wasit University, College of Administration and Economics, Statistics Department, Wasit, Iraq R. Adnan Jaleel Al-Nahrain University, Department of Information and Communication Engineering, Baghdad, Iraq Musaddak M. A. Zahra Unvirsity of Babylon, Department of Electrical Engineering, Babylon, Iraq This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work. 2022 267 271 1276 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.190122 https://www.americaspg.com/journal/21/article/1276 https://www.americaspg.com/storage/9297.pdf