A Framework for General Conformable Fractional Grey System Models: A Physical Perspective and its Actual Application

Grey system theory is an important mathematical tool for describing uncertain information in the real world. It has been used to solve the uncertainty problems specially caused by lack of information. As a novel theory, the theory can deal with various fields and plays an important role in modeling the small sample problems. But many modeling mechanisms of grey system need to be answered, such as why grey accumulation can be successfully applied to grey prediction model? What is the key role of grey accumulation? Some scholars have already given answers to a certain extent. In this paper, we explain the role from the perspective of complex networks. Further, we propose generalized conformable accumulation and difference, and clarify its physical meaning in the grey model. We use our newly proposed fractional accumulation and difference to our generalized conformable fractional grey model, or GCFGM(1,1), and employ practical cases to verify that GCFGM(1,1) has higher accuracy compared to traditional models.