International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3313 2020 2020 Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan Kamel Kamel Department of Mathematics, Al-Gunfudah University College, Umm Al-Qura University, Mecca 21955, Saudi Arabia Adel Almalki Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan Amer H. Darweesh Department of Mathematics & Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan Amal Sawalmeh 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 2025 398 416 10.54216/IJNS.250335 https://www.americaspg.com/articleinfo/21/show/3313