Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making

The time fractional Black–Scholes equation (TFBSE) is designed to evaluate price fluctuations within a correlated fractal transmission system. This model prices American or European put and call options on non-dividend-paying stocks. Reliable and efficient numerical techniques are essential for solving fractional differential models due to the global characteristics of fractional calculus. This paper focuses on the numerical solution for the TFBSE for American and European option pricing models by means of the local meshless radial basis function (RBF) interpolation. This problem is temporally approximated using a finite difference scheme with 2−β order accuracy for 0