In this work the Monte Carlo method is introduced for numerical evaluation of fractional-order derivatives. A general framework for using this method is presented and illustrated by several examples. The proposed method can be used for numerical evaluation of the Grünwald-Letnikov fractional derivatives, the Riemann-Liouville fractional derivatives, and also of the Caputo fractional derivatives, when they are equivalent to the Riemann-Liouville derivatives. The proposed method can be enhanced using standard approaches for the classic Monte Carlo method, and it also allows easy parallelization, which means that it is of high potential for applications of the fractional calculus.

在这项工作中，蒙特卡罗方法被引入用于分数阶导数的数值评估。通过几个示例介绍并说明了使用此方法的一般框架。当 Grünwald-Letnikov 分数阶导数、Riemann-Liouville 分数阶导数以及 Caputo 分数阶导数等价于 Riemann-Liouville 导数时，所提出的方法可用于数值评估。所提出的方法可以使用经典蒙特卡罗方法的标准方法进行增强，并且它还允许轻松并行化，这意味着它在分数微积分的应用中具有很高的潜力。