In this paper, we investigate a new version of stock model under uncertain circumstances for uncertain stock markets. Firstly, solutions to some uncertain fractional differential equations are presented by employing the Mittag-Leffler function. Then, a new uncertain stock model with mean-reverting process is formulated on the basis of uncertain fractional differential equations. Finally, European option pricing formulas based on the proposed model are investigated as well as some numerical examples.

中文翻译：

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基于不确定分数阶微分方程的欧式期权定价模型

在本文中，我们针对不确定的股票市场研究了在不确定情况下的股票模型的新版本。首先，利用Mittag-Leffler函数给出了一些不确定分数阶微分方程的解。然后，在不确定的分数阶微分方程的基础上，建立了具有均值回复过程的不确定股票模型。最后，研究了基于所提出模型的欧洲期权定价公式以及一些数值示例。