aspg-21-1787-1791475501 20261008160501 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 1 Sahar M. Jabbar Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq Ameera N. Alkiffai Department of Mathematics, College of Education for Girls, University of Kufa, Najaf, Iraq Azal Mera Department of Mathematics, College of Education for Girls, University of Kufa, Najaf, Iraq In this paper, a new fuzzy integral transform is introduced and called “fuzzy Mohand transform” which is based on a mathematical formula of the classical Mohand transform. The fuzzy technique that is well-established from fuzzy Laplace transform, agrees with the neutrosophic logic. In fact, in mathematical field, neutrosophic logic, which is based on the idea of indeterminacy, is introduced as a generalization of fuzzy logic. In Neutrosophic logic, there are three values, grade of membership of Truth values (T), Indeterminate values (I) and False values (F). To demonstrate this mixed technique, a realistic example about heating system is discussed as an illustrative example for solving an ordinary differential equation of first order using fuzzy Mohand transform with neutrosophic numbers as an initial condition. 2023 08 13 1787 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210101 https://www.americaspg.com/journal/21/article/1787 https://www.americaspg.com/storage/11683982035.pdf