  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.
