International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1787 2020 2020 Department of Mathematics, College of Education for Pure Science, University of Babylon, Babil, Iraq Sahar M. Jabbar Department of Mathematics, College of Education for Girls, University of Kufa, Najaf, Iraq Ameera N. Alkiffai Department of Mathematics, College of Education for Girls, University of Kufa, Najaf, Iraq Azal Mera 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 2023 08 13 10.54216/IJNS.210101 https://www.americaspg.com/articleinfo/21/show/1787