In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution.

中文翻译：

---

分数阶Black-Scholes-Schrodinger方程的RBFs数值解

本文采用径向基函数（RBFs）方法求解金融问题期权定价中的分数Black-Scholes-Schrodinger方程。RBFs方法用于离散化空间导数过程。在Caputo的意义上，时间分数导数的近似值是通过一个简单的正交公式来解释的。该RBFs方法在两个数值示例的不同问题上得到了理论证明：时间步长套利泡沫案例和时间线性套利泡沫案例。然后，在分数阶接近1的情况下，将数值结果与半经典解进行比较。结果，两个数值示例均表明，RBFs方法的期权价格满足半经典解。