Uncertain fractional differential equation (UFDE) is a kind of differential equation about uncertain process. As an significant mathematical tool to describe the evolution process of dynamic system, UFDE is better than the ordinary differential equation with integer derivatives because of its hereditability and memorability characteristics. However, in most instances, the precise analytical solutions of UFDE is difficult to obtain due to the complex form of the UFDE itself. Up to now, there is not plenty of researches about the numerical method of UFDE, as for the existing numerical algorithms, their accuracy is also not high. In this research, derive from the interval weighting method, a class of fractional adams method is innovatively proposed to solve UFDE. Meanwhile, such fractional adams method extends the traditional predictor-corrector method to higher order cases. The stability and truncation error limit of the improved algorithm are analyzed and deduced. As the application, several numerical simulations (including $\alpha$-path, extreme value and the first hitting time of the UFDE) are provided to manifest the higher accuracy and efficiency of the proposed numerical method.

翻译：不确定分数阶微分方程是关于不确定过程的一类微分方程。作为描述动态系统演化过程的重要数学工具，由于具有遗传性和记忆性特征，UFDE优于整数阶常微分方程。然而，在大多数情况下，由于UFDE自身形式的复杂性，很难获得其精确解析解。目前关于UFDE数值方法的研究尚不充分，而现有数值算法的精度也不高。本研究从区间加权法出发，创新性地提出了一类分数阶Adams方法来求解UFDE。同时，该分数阶Adams方法将传统的预测校正法推广到了高阶情形。对改进算法的稳定性和截断误差极限进行了分析和推导。作为应用，提供了若干数值模拟（包括UFDE的α-路径、极值和首达时间）来证明所提数值方法的高精度和高效率。