In this paper, we consider direct problem and inverse source problem of time‐fractional Black‐Scholes type model involving hyper‐Bessel operator. Analytical solutions to these problems are constructed based on appropriate eigenfunction expansion and Erdélyi‐Kober fractional integrals whose kernel has double singularities; then, existence and uniqueness are established. At last, the results are demonstrated by explicit solutions of some examples using appropriate choice of the given data.

中文翻译：

---

涉及超贝塞尔算子的时间分数维Black-Scholes型方程解析解的存在唯一性

在本文中，我们考虑了涉及超贝塞尔算子的时分形Black-Scholes型模型的直接问题和逆源问题。这些问题的解析解是基于适当的本征函数展开和核具有双奇点的Erdélyi-Kober分数积分构建的；然后，建立存在性和唯一性。最后的结果是通过使用给定的数据的适当选择一些例子明确的解决方案证明。