This paper develops a joint framework for the fractional diffusion equation driven by Lévy processes within a stochastic volatility setting, serving as an extension of the classical Heston model. We present the mathematical foundations of the model, emphasizing the dynamics of asset prices influenced simultaneously by fractional Brownian motion, which introduces long memory, and Lévy processes, which capture discontinuous jumps. The integration of these components allows the model to account for both fat-tailed and skewed return distributions. A Fourier transform representation is derived for option pricing under this generalized framework, and a Monte Carlo simulation scheme is proposed to numerically evaluate the associated stochastic integrals. Furthermore, maximum likelihood estimation (MLE) is employed for parameter estimation, and a systematic procedure for applying the proposed model to empirical financial data is outlined. The results demonstrate that the model provides a more realistic representation of market dynamics than classical approaches, particularly in explaining volatility clustering, extreme events, and the heavy-tailed nature of financial returns. Overall, the fractional diffusion–Lévy process framework offers a robust alternative for both theoretical research and practical applications in financial modeling.
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