Fractional grey model based on non-singular exponential kernel and its application in the prediction of electronic waste precious metal content

Precious metal recovery is the main economic power of electronic waste (e-waste) recovery. The prediction of e-waste and its precious metal content is of great significance to the realisation of China's circular economy. In this work, the generation mechanism of e-waste is firstly deduced to determine model characteristics suitable for its prediction. Fractional derivative grey models base on a weak singular power kernel function (PFGM(q,1)) and a non-singular exponential kernel function (EFGM(q,1)) are established. Compared with the PFGM(q,1), the EFGM(q,1) has the advantages of simpler solution, lower calculation complexity and wider scope of application. Next, some data are selected to verify the validity. The EFGM(q,1) is used to predict mobile phone, laptop, desktop and television waste, and the weight of printed circuit boards (PCBs) in the waste and content of precious metals in these PCBs are calculated. Finally, the trend of e-waste and its precious metal contents are analysed and discussed based on the calculation results.