Fractional-Order Accumulative Gray Model for Carbon Emission Prediction: A Case Study of Shandong Province

Against the backdrop of global climate change, accurate prediction of carbon emissions is crucial for formulating effective emission reduction policies. Utilizing data from the China Energy Statistical Yearbook and the Shandong Statistical Yearbook between 2010 and 2022, this study estimates carbon emissions in Shandong Province from 2016 to 2022 using the carbon emission factor method and projects future trends through the fractional-order accumulated grey model FAGM(1,1). The forecast results indicate that both total carbon emissions and per capita carbon emissions in Shandong will follow a trajectory characterized by ‘slow increase-peak-steady decline’, while carbon emission intensity is expected to decrease consistently year by year. Based on these projections, this study proposes that Shandong should accelerate the optimization of its energy supply structure to establish a clean and low-carbon energy system, promote green transformation and upgrading of industries to cultivate new economic growth drivers, and enhance policy-market coordination mechanisms to strengthen institutional incentives and constraints. These findings provide a scientific basis for Shandong to achieve its carbon peak and carbon neutrality goals and also offer methodological references for other industrialized provinces facing similar challenges.