Abstract
In this manuscript, the rumours spreading model in the social network is analysed associated with the classical-Caputo piecewise derivative. The existence and uniqueness of a solution are examined for the aforementioned problem. The suggested problem's approximate solution is found using the piecewise numerical iterative Newton polynomial approach. The numerical simulations for the piecewise derivable problem under consideration are presented using the data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer. The validity of the model is confirmed by simulating real data with simulated data which are taken from the literature.