Finite‐time extinction of a fractional rumor model

Rumors often exist in real life. If rumors are not controlled, they usually do not disappear for a limited time. Meanwhile, everyone has memories and time‐fractional derivative can describe the memories. Thus, in this paper, a new time‐fractional rumor model is introduced, and moreover, the finite time extinction of rumor is obtained under a distributed controller is added. What's more, both the ordinary differential equations model and partial differential equations model are studied. Numerical examples verify our results.