TIME-FRACTIONAL DYNAMICS MODEL BLACK–SCHOLES: IMPLICATIONS FOR OPTION PRICING STABILITY

The primary objective of this study is to analyze the Hyers–Ulam stability of fractional derivatives for the Black–Scholes model, involving two underlying asset systems and utilizing Caputo fractional derivatives. We employ a fixed-point approach to examine the existence and uniqueness of solutions and to investigate the Hyers–Ulam stability of the given problem. Additionally, we analyze the graphical behavior of the obtained results, demonstrating that the analytical method is highly efficient and delivers precise results for determining approximate numerical solutions. The findings highlight the significant role of fractional approaches in studying nonlinear systems of scientific and physical importance. Furthermore, the graphical analysis, considering various fractional orders and parameter values, unveils new insights and intriguing phenomena associated with the Black–Scholes model.