 We developed a method for solving the Newell-Whitehead Siegel model with caputo derivatives using Sumida Transform and residual power series method, RPSM, which generates a series solution through iterations based on initial conditions, demonstrating high accuracy and validity without significant calculation or element restrictions. The results are visualized through 2D and 3D graphs. This article was authored by Jinxing Liu, Mohammed Nadim, and Yehya Al Sayed.