This study presents the application of the New Iterative Method (NIM) to solve the fractional Wu-Zhang equation under the Caputo derivative operator. The method is effective for obtaining approximate solutions to fractional differential equations. The research investigates the behavior of the Wu-Zhang equation, which describes nonlinear water waves in shallow waters. The equation has been extended to include time-fractional and space-fractional derivatives, leading to the time-fractional and space-fractional Wu-Zhang systems. The study applies the NIM to solve the fractional Wu-Zhang equation and analyzes the behavior of the solutions under different fractional orders. The results show that the NIM provides accurate and efficient solutions for the fractional Wu-Zhang equation. The study also compares the approximate solutions obtained using NIM with the exact solutions, demonstrating the method's effectiveness. The results are visualized using 3D and 2D plots, and tables are provided to compare the numerical solutions with the exact solutions. The study concludes that the NIM is a valuable tool for solving fractional-order differential equations and has potential applications in various scientific and engineering fields. The research is supported by financial funding from King Khalid University and King Faisal University. The authors declare no conflict of interest.This study presents the application of the New Iterative Method (NIM) to solve the fractional Wu-Zhang equation under the Caputo derivative operator. The method is effective for obtaining approximate solutions to fractional differential equations. The research investigates the behavior of the Wu-Zhang equation, which describes nonlinear water waves in shallow waters. The equation has been extended to include time-fractional and space-fractional derivatives, leading to the time-fractional and space-fractional Wu-Zhang systems. The study applies the NIM to solve the fractional Wu-Zhang equation and analyzes the behavior of the solutions under different fractional orders. The results show that the NIM provides accurate and efficient solutions for the fractional Wu-Zhang equation. The study also compares the approximate solutions obtained using NIM with the exact solutions, demonstrating the method's effectiveness. The results are visualized using 3D and 2D plots, and tables are provided to compare the numerical solutions with the exact solutions. The study concludes that the NIM is a valuable tool for solving fractional-order differential equations and has potential applications in various scientific and engineering fields. The research is supported by financial funding from King Khalid University and King Faisal University. The authors declare no conflict of interest.