Advanced semi-analytical techniques for the q-fractional Ivancevic option pricing model - Khalid K. Ali; Mohamed S. Mohamed; M. Maneea (Ain Shams Engineering Journal, 2025)
This study investigates the q-fractional Ivancevic option pricing model using two advanced semi-analytical methods: the q-Laplace Residual Power Series Method (q-LRPSM) and the q-Homotopy Analysis Method (q-HAM). The q-LRPSM is introduced and adapted for the first time to solve q-fractional partial differential equations, offering accurate and efficient approximate solutions through a power series approach. The q-HAM builds on the traditional HAM by constructing a homotopy between an initial guess and the exact solution. Numerical simulations confirm the effectiveness and accuracy of both methods across various q-values and time steps, with 2D and 3D visualizations highlighting their rapid convergence. The study demonstrates that these methods provide a powerful framework for solving complex models in financial mathematics and applied sciences.