Interaction-based differential dynamic fractional-order IDFGM(1,N,ri) model and its applications

Purpose This study aims to address the interaction among influencing factors in real systems and the varying intensity of the impact that independent variables have on dependent variables, a new IDFGM(1,N,ri) model is proposed. Design/methodology/approach Firstly, grey relational analysis is utilized to screen the sequences of influencing factors and identify their interactions. Secondly, particle swarm optimization is employed for differential optimization of the orders and nonlinear parameters of each variable, while the least squares method is used to calculate the structural parameter matrix, constructing time response function of the model. Finally, the model is applied to simulate and predict carbon dioxide emissions in China and is compared with other models. Findings The results show that the IDFGM(1,N,ri) model has good simulating and predicting performance, verifying its effectiveness. The newly introduced model demonstrates a high degree of compatibility and can be seamlessly integrated with conventional grey models. In the case analysis, the IDFGM(1,N,ri) model shows enhanced predictive performance relative to the benchmark model. This finding suggests that the model articulated in this study successfully captures the nonlinear attributes of each sequence by employing differential optimization of the order, facilitated by the particle swarm optimization algorithm. Practical implications This article presents a scientifically grounded and effective model for forecasting carbon dioxide emissions. The outcomes of these predictions can serve as a theoretical foundation for the development of policies aimed at carbon reduction and energy transition. Originality/value The unique contribution of this article is the incorporation of interactions into multivariable prediction models, along with the optimization of the cumulative sequence of both dependent and independent variables to account for variations. Furthermore, the application of particle swarm optimization has enabled the model to adapt dynamically.