After the aging of lithium batteries, the relationship between the external characteristics of battery and the state of charge is changed, resulting in a model mismatch and a decrease in the accuracy of battery state of charge estimation, and it is necessary to re-identify the model parameters. On the other hand, in the real scenario, it is difficult to obtain a large amount of aging data, and the fractional-order multidimensional Taylor network model obtained by using only a small amount of sample data for training may suffer from poor generalization performance. In this paper, we combine the fractional-order multidimensional Taylor network with the mean-maximum difference method, use the existing lithium battery as the source domain data, lithium battery aging data as the target domain, calculate the difference between the target domain and the source domain, and obtain knowledge from the source domain to apply it to the target domain to reduce the dependence of the FMTN model on the amount of data. The results of the experiments show that the estimation accuracy of the method proposed in this paper is 64.7% higher than the direct training of the fractional-order multidimensional Taylor network.