AbstractIn this investigation, we propose a numerical method based on the fractional‐order generalized Taylor wavelets (FGTW) for option pricing and the fractional Black–Scholes equations. This model studies option pricing when the underlying asset has subdiffusive dynamics. By applying the regularized beta function, we give an exact formula for the Riemann–Liouville fractional integral operator (RLFIO) of the FGTW. An error analysis of the numerical scheme for estimating solutions is performed. Finally, we conduct a variety of numerical experiments for several standard examples from the literature to assess the efficiency of the proposed method.