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.

贵金属回收是电子废物（电子废物）回收的主要经济动力。电子废物及其贵金属含量的预测对实现我国循环经济具有重要意义。在这项工作中，首先推导电子废物的产生机理，以确定适合其预测的模型特征。分数衍生物灰色模型基础上的弱奇异功率核函数（PFGM（q，1））和一非奇异指数核函数（EFGM（q，1））成立。与PFGM（相比q，1），将EFGM（q，1）具有更简单的解决方案的优点，降低计算复杂度和应用的范围更广。接下来，选择一些数据以验证有效性。EFGM（q，1）用于预测手机，笔记本电脑，台式机和电视的废物，并计算废物中印刷电路板（PCB）的重量以及这些PCB中贵金属的含量。最后，根据计算结果对电子垃圾的趋势及其贵金属含量进行了分析和讨论。