<p>This study looks at how rumors spread, especially online, where false information can quickly spread to millions of people, disrupt public order, infringe on privacy, and endanger public safety. A dishonest user targets friends and strangers with marketing accounts on mobile social networking sites to propagate rumors. In this article, we propose a fractional order nonlinear mathematical framework explaining how rumors spread widely on Facebook and Twitter about different life interest topics with the Caputo operator. For the fractional-order Caputo model, there is an analytical solution verified with the Lipchitz condition for boundedness, positivity, and feasible solutions. The existence and uniqueness of solutions are established using the Banach contraction principle. We conduct qualitative analyses to validate the model and assess control efficiency by calculating the fundamental reproductive number. Additionally, we identify equilibrium points for rumor-free situation. Chaos control will use the regulate for linear responses approach to stabilize the system according to its equilibrium points. The global stability of equilibrium points is confirmed using the Lyapunov function. A numerical iterative approach based on the Newton polynomial interpolation is employed for the numerical approximation of the proposed problem. Numerical simulations have been conducted to illustrate the superior performance of the fractional-order model at different fractional-order values and the surface face graph shows the complete dynamics of rumor propagation in a time scale frame for different factors. This model can capture all historical information of the system under consideration, a capability not present in classical (integer-order) differential equations. The results, which are backed up by graphical representations, show how well the novel method solves this fractional model and how useful it is in combating the spread of rumors.</p>