<p>In this paper, we consider the time-fractional Kuramoto–Sivashinsky model as a fundamental nonlinear partial differential equation that plays an important role in understanding pattern formation, turbulence, and chaos theory. To solve this complex equation more effectively, we propose a new collocation method based on shifted companion Morgan–Voyce polynomials and reformulate the equation into a nonlinear system. After computing the operational matrices of partial derivatives, we select collocation points and obtain a set of nonlinear equations that significantly improve the accuracy and adaptability of the derived approximations. Moreover, we discuss the stability and convergence analysis of the proposed method and prove that the residual term of the numerical method tends to zero. The numerical experiments obtained emphasize the correctness of the theoretical findings, showing strong convergence and reliability for various coefficient scenarios, indicating that collocation methods utilizing shifted companion Morgan–Voyce polynomials can substantially enhance the resolution of time-fractional partial differential equations.</p>