Fractional Differential Equation Modeling of User Online Purchase Behavior Analysis

• Mingyue Bai,

Vol. 19, No. 5, May 31, 2025
10.3837/tiis.2025.05.006, Download Paper (Free):

• fractional differentiation
• online shopping
• purchase behaviour
• user query

Abstract

Online user purchase behaviour varies with the consumer’s choice, interest, and product requirements. A deep analysis of such behaviour is useful in providing user recommendations based on products and their demands. This article proposes a Differential Model using Purchase Behavior (DM-PB) to provide a comprehensive insight into user recommendations. This proposed method relies on the user search query and recurring recommendations throughout the purchase session. The two factors are differentiated throughout the purchase session for maximum and nil occurrences. The recommendations for the current and similar queries are deviated based on the mean fraction. Therefore, the differentiation is instigated from the mean fraction to the maximum occurrence until user satisfaction with the session is achieved. The differential extractions beneath the mean fractions based on query and recommendations are declined for trimming and converging towards the consumer’s demands. The differentiation process pursues a fractional mathematical model for mean variation between maximum and nil occurrences. This method incorporates the previous differentiated mean for further recommendations across user queries. The proposed method improves the recommendation ratio by 14.55%, user satisfaction estimation by 10.05%, and reduces variation by 10.54%, query processing complexity by 10.05%, and processing time by 9.84% compared to existing models.

Statistics

Cite this article