Diverse soliton solutions to the conformable Ivancevic option pricing model via the modified generalized Riccati equation mapping method

In this paper, we employ the modified generalized Riccati equation approach to derive a variety of exact solutions for the Ivancevic option pricing model incorporating the conformable derivative. The Ivancevic option pricing equation is structured using an adaptive nonlinear Schrödinger equation, which describes the option-pricing wave function based on time and stock price. This equation captures the typical regulated Brownian motion seen in financial markets. The predictive nature of the model allows financial analysts to forecast option prices under varying market conditions. The model helps traders to price complex options with greater accuracy by considering nonlinear market dynamics. A variety of soliton solutions to the conformable Ivancevic model are derived, including dark, mixed dark–bright, singular, bell-shaped, and wave solutions. To provide deeper insights into their dynamical properties and physical significance, these solutions are visualized through three-dimensional plots, two-dimensional plots, and contour plots. The graphical representations underscore the intricate dynamics and potential financial applications of soliton solutions within the conformable framework, demonstrating their relevance in option pricing theory and nonlinear financial modeling.