  This study enhances option pricing by presenting unique pricing model
fractional order Black-Scholes-Merton (FOBSM) which is based on the
Black-Scholes-Merton (BSM) model. The main goal is to improve the precision and
authenticity of option pricing, matching them more closely with the financial
landscape. The approach integrates the strengths of both the BSM and neural
network (NN) with complex diffusion dynamics. This study emphasizes the need to
take fractional derivatives into account when analyzing financial market
dynamics. Since FOBSM captures memory characteristics in sequential data, it is
better at simulating real-world systems than integer-order models. Findings
reveals that in complex diffusion dynamics, this hybridization approach in
option pricing improves the accuracy of price predictions. the key contribution
of this work lies in the development of a novel option pricing model (FOBSM)
that leverages fractional calculus and neural networks to enhance accuracy in
capturing complex diffusion dynamics and memory effects in financial data.
