Rumor spreading is a trivial social practice, which has a long history of
affecting society both in a positive and negative way, and modelling of transmission
of rumors has been an attractive area for social and, of late, for physical scientists. In
this chapter, we have modified the rumor-spreading model by incorporating fractional
derivatives in the Caputo sense. To analyze the spread of rumors in social as well as
virtual networks, we have considered four populations, namely, ignorant, spreader,
recaller, and stifler. The existence and uniqueness, and boundedness of the solutions
of the present model have been exhibited theoretically. Numerically, we have
experimented with the effect of fractional derivatives and the density of one
population on the other population by demonstrating the impact of rumor spread with
the change of various parameters.
Keywords: Adams-Bashforth-Moulton method, Caputo fractional derivative, Mathematical model, Rumor spreading.
