This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.

中文翻译：

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时间分数Black-Scholes方程的新型数值格式

本文由两部分组成。一方面，研究了时间分数阶Black-Scholes方程解的正则性。另一方面，为了克服初始层的困难，基于变量的变化提出了改进的L 1时间离散化。通过使用Chebyshev Galerkin方法完成空间离散化。获得了全离散方案的最佳误差估计。最后，给出了一些数值结果以证实理论结果。