  As an essential characteristics of fractional calculus, the memory effect is
served as one of key factors to deal with diverse practical issues, thus has
been received extensive attention since it was born. By combining the
fractional derivative with memory effects and grey modeling theory, this paper
aims to construct an unified framework for the commonly-used fractional grey
models already in place. In particular, by taking different kernel and
normalization functions, this framework can deduce some other new fractional
grey models. To further improve the prediction performance, the four popular
intelligent algorithms are employed to determine the emerging coefficients for
the UFGM(1,1) model. Two published cases are then utilized to verify the
validity of the UFGM(1,1) model and explore the effects of fractional
accumulation order and initial value on the prediction accuracy, respectively.
Finally, this model is also applied to dealing with two real examples so as to
further explain its efficacy and equally show how to use the unified framework
in practical applications.
