<p>This paper introduces a high-accuracy numerical collocation scheme for solving fractional-order differential equations. The model problem considered is the general multi-term linear fractional differential equation under Caputo derivatives. The key contribution of this work is the development of a novel framework based on fractional shifted orthogonal Vieta-Fibonacci functions (FSVFF). The method’s innovation lies in expanding the equation’s highest-order derivative as a finite series of FSVFF. Operational matrices are then derived to perform iterative integration, systematically constructing the full approximate solution. The entire process leverages direct approximations of the Caputo fractional derivative and Riemann–Liouville integral, which, combined with the collocation technique, transforms the original fractional problem into a tractable system of linear equations. A rigorous convergence analysis is provided to establish the theoretical foundation of the method. Its numerical efficacy is validated through three distinct examples, where superior accuracy and computational efficiency are demonstrated compared to four existing alternative methods.</p>