International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3420 2020 2020 Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan admin admin Department of Mathematics, Al-Gunfudah University College, Umm Al-Qura University, Mecca 21955, Saudi Arabia Adel Almalki Department of Material Engineering - College of Engineering, Shatrah University Thi-Qar 64001 - Iraq Mahmood Shareef Ajeel Department of Mathematics-Faculty of Science, Philadelphia University, Amman 19392- Jordan Azza I. Abu Abu-Shams Department of Mathematics-Faculty of Science, Philadelphia University, Amman 19392- Jordan Sajeda El El-bashabsheh This paper presents a modified Laplace Adomian decomposition method (MLADM) to solve the nonlinear time-fractional coupled Jaulent–Miodek system. The proposed approach provides convergent series solutions with easily computable components, demonstrating both accuracy and simplicity in its application. By employing the Caputo fractional derivative, this study establishes a robust framework for analyzing nonlinear behavior in fractional differential equations. The effectiveness of the method is validated through comparisons with previous studies, with results illustrated using graphical representations. The solutions proposed herein are significant for modeling complex and dynamic real-world phenomena across various scientific disciplines. All computations and graphical results were carried out using Mathematica, emphasizing the method’s reliability, precision, and ease of application to nonlinear fractional systems. The study of fractional nonlinear systems is crucial for modeling complex, dynamic, and uncertain processes, which are core aspects of neutrosophic science. By addressing the intricate behavior of the nonlinear time-fractional coupled Jaulent–Miodek system, this work advances mathematical models that encapsulate uncertainty, indeterminacy, and complex interactions. Such an alignment with the principles of neutrosophic science underscores the relevance of our approach to the objectives of the International Journal of Neutrosophic Science, highlighting its potential to enhance the understanding and practical applications of complex systems. 2025 2025 42 57 10.54216/IJNS.250405 https://www.americaspg.com/articleinfo/21/show/3420