Fractional-order rumor propagation model with memory effect

The harm of online rumor cannot be ignored, and the research on its spreading mechanism is the core issue of rumor governance. People’s judgment on whether information is a rumor is affected by early memory. In order to simulate the spread process of rumors better, so as to timely control rumors, this paper establishes a fractional rumor propagation model with memory effect based on the SIR rumor propagation model. Then, the basic regeneration number of the model is calculated, and the stability analysis of the equilibrium point is performed. Finally, the model is solved and simulated using an efficient and high-precision numerical solution algorithm. It was found that the lower the order, the stronger the memory effect. The simulation results show that the fractional-order rumor propagation model can be used to study the rumor propagation process more realistically. By enhancing the memory effect, the rumor propagation scale can be reduced and the harm of rumor can be reduced. The difference between this study and the past is that the fractional differential equation is used to describe the influence of memory effect on rumor propagation.