This research presents a novel and robust analytical approach to investigate the mathematical solution of the time-fractional Black–Scholes (BS) model using the Caputo fractional derivative. We propose the Mohand Perturbation Transform Scheme (MPTS), which incorporates the Mohand integral Transform (Formula: see textT) with the Homotopy Perturbation Scheme (HPS). This technique determines the series coefficients and minimizes the error distribution using the symbolic computation software. The obtained results are expressed in a rapidly convergent series form and show strong agreement with the exact solutions. Visual analyses are also provided to highlight the practical behavior of the model. The findings indicate that the proposed scheme is simple, appropriate, and effective for solving and interpreting a wide class of nonlinear models arising in physical phenomena.
Luo et al. (Sat,) studied this question.