Network Public Opinion Prediction Based on Conformable Fractional Non-homogeneous Discrete Grey Model

the traditional grey model assumes that the original data series conforms to the homogeneous exponential trend rather than the non-homogeneous exponential trend. However, compared with the integer-order gray model, the fractional-order gray model is more efficient and flexible in time series forecasting. Hence, in this paper, a conformable fractional order calculus is introduced to extend the integer order gray model into a fractional order gray model. A conformable fractional non-homogeneous exponential discrete grey model (abbreviated as CFNDGM) is proposed, and the particle swarm algorithm is further developed to optimize its order. Specifically, we first use the Baidu index generated by "Xi'an Epidemic" and "MU5735" to build a model. Then use the least squares method to solve the model parameters, obtain the predicted simulation value through the response expression, and finally obtain the data prediction result. The simulation validates that the prediction accuracy of the fractional order non-homogeneous grey model is higher than that of the integer order non-homogeneous grey model.