User online consumption behaviour based on fractional differential equation

User consumption behaviour is a subject worthy of study. Because consumers’ consumption behaviours are dynamic and with individual differences, various factors need to be considered when establishing a fractional differential equation model of users’ online consumption behaviour. The two elements, namely advertising and price are more evident in influencing consumer behaviour. Therefore, the paper establishes a product diffusion fractional differential equation model of price and advertising presence or absence to study the impact of these two factors on consumer behaviour. It turns out that ignoring the advertisement and the cost of the product is related to the characteristics of the consumer network. When there are advertising and price factors, product awareness is related to price constraints.