Fractional Bass Diffusion Model

The innovation dilation or contract of the Bass diffusion model is equivalented to the fractional power of imitation probability function.

To illustrate the application of the Bass model in practice, we chose online education as a specific case of educational digital transformation and estimate the temporal model of its diffusion process. The cumulative numbers of online education users from 2001 to 2022 were collected from the "China Internet Development Statistics Report" published by the China Internet Network Information Center and third-party industry research reports. Using these data, we calculate the number of new users each year. Due to the influence of disruptive events such as the COVID-19 pandemic from 2020 to 2022, we firstly used data from 2001 to 2019 to create the linear model, and then use the fractional correction term to find the lowest mean square error fit when the COVID-19 pandemic from 2020 to 2022 data are also included. This way, we can obtain both optimistic and pessimistic predictions.