With the development of the times and the progress of science and technology, the financial market is constantly reformed and China's financial industry is gradually modernized. However, China's economy has been in the stage of rough growth for a long time, which has led to low efficiency in the allocation of financial resources and unreasonable use of funds, and this has seriously restricted the whole social production activities and the stability and sustainable and healthy development of the national economy, so the prevention and control of financial risks is particularly important. Therefore, how to identify and measure the risks in China's financial industry and manage and invest them in a reasonable way is a very serious issue facing China's financial institutions today. On the other hand, due to the continuous development and innovation of the financial market, China's financial industry has been gradually reformed. However, due to the imperfection of China's economic system and related laws and regulations, some non-performing assets and irregularities in the operation of domestic financial institutions have emerged, and instability in the financial market has also emerged. These phenomena make China's financial industry face huge financial risks in the process of development.

How to find books suitable for them from the massive book information is a problem that needs to be considered at present for university library users. This paper proposes a personalized recommendation system for digital libraries utilizing fractional differential equations. At the same time, we use the idea of a collaborative filtering algorithm to recommend books for new users. Finally, we use the accurate data of the library to design a personalized book recommendation system for university libraries. The research shows that the university library lending system based on fractional differential equations has improved user experience.