<p>The Newell-Whitehead-Segel model, also known as the NW-S model, is a mathematical model used to describe pattern formation in systems exhibiting spatially extended dynamics. Particularly, it is famous for its application in the study of chemical reaction-diffusion systems, where it has been used to explain the formation of spatial patterns such as stripes, spots, and spirals. These patterns can emerge in systems where the diffusion of substances interacts with chemical reactions occurring in the medium. This article presents a novel numerical approximation to the fractional-ordered NW-S equation. The suggested system, the rank polynomial collocation method (RPCM), is created based on the functional basis of rank polynomials of star graphs and the well-posed operational matrices of integration of rank polynomials. The time derivative is derived in the Caputo sense. The purported RPCM approach generates a system of nonlinear algebraic equations from the nonlinear time-fractional Newell-Whitehead-Segel equation (TNW-SE). The Newton-Raphson method is used to solve the resulting system, yielding an approximate solution to the nonlinear TNW-SE. The technique’s validity and efficacy are demonstrated using numerical examples. The acquired numerical results are reasonably consistent with those published in the literature, as explained in the tables and figures. Further, the standard error norms quantitatively evaluate accuracy and convergence, confirming the resilience of RPCM in addressing both classical and fractional cases. RPCMs adaptability implies that it has greater relevance to hierarchical graph structures and fractional-order models, with potential developments in adaptive refinement procedures to enhance solution accuracy. Potential expansions could focus on improving computing efficiency, particularly through the integration of machine learning for large-scale multidimensional systems, thereby enabling more precise and scalable numerical solutions.</p>