Since the concept of uncertain fractional differential equations was proposed, its wide range of applications have urged us to consider parameter estimation for uncertain fractional differential equations. In this paper, based on the definition of Liu process, we construct a function of unknown parameters which follows a standard normal uncertainty distribution. Then the method of moments is used to build a system of equations whose solutions are the estimated values of unknown parameters. After that, an algorithm of parameter estimation for a special uncertain fractional differential equation is proposed. Finally, the algorithm is applied to two numerical examples and the acceptability of the estimated parameters is proved by using uncertain hypothesis test.

自不确定分数微分方程的概念被提出以来，其广泛的应用促使我们考虑不确定分数微分方程的参数估计。在本文中，基于刘过程的定义，我们构造了一个遵循标准正态不确定性分布的未知参数函数。然后使用矩量法建立一个方程组，其解是未知参数的估计值。然后，提出了一种特殊的不确定分数阶微分方程的参数估计算法。最后将该算法应用于两个数值实例，并通过不确定假设检验证明了估计参数的可接受性。