aspg-21-3313-1791468602 20261008141002 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Kamel Al-Khaled Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan Adel Almalki Department of Mathematics, Al-Gunfudah University College, Umm Al-Qura University, Mecca 21955, Saudi Arabia Amer H. Darweesh Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan Amal Sawalmeh Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan In order to solve hyperbolic fractional partial differential equations, this paper develops the Sumudu decomposition method. This method is based on solving time-fractional hyperbolic partial differential equations either individually or in systems using the Sumudu transform. Adomian polynomials whose values are chosen by a specific formula are used to solve the non-linear terms. The developed method’s convergence and stability are discussed. Example such as the shallow water equations, which serve as illustrations of the fractional derivatives as defined by Caputo, is used to show the validity and applicability of the proposed method. It is discovered that the procedure is rapid and precise 2025 398 416 3313 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250335 https://www.americaspg.com/journal/21/article/3313 https://www.americaspg.com/storage/41731624735.pdf