<p>In this paper, an optimization method based on the generalized shifted Chebyshev polynomials is developed to solve the time-fractional Black-Scholes model for European options. To this end, a fractional derivative matrix is derived for these functions. In the proposed method, by expanding the solution of the problem using these polynomials as basis functions and applying an optimization technique based on the Lagrange multipliers technique, the original problem is transformed into an algebraic system of equations. The solution of this system provides the unknown matrix, which is used to obtain the approximated numerical solution. The accuracy of the established approach is investigated and compared with other numerical methods by solving several numerical examples. The results demonstrate that the proposed technique is highly accurate for this problem. The novelty of this study lies in the application of generalized polynomials to the time-fractional financial model, which advances not only by improving the accuracy of the fractional financial model but also by opening new avenues for tackling complex financial challenges in the future.</p>