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Abstract In this work, we will study the late-time dynamic evolution of the F(R) gravity dark energy model of an interaction between dark radiation and dark matter. We explore the possibility of the apparent extra dark radiation being linked directly to the physics of cold dark matter (CDM). In particular, we consider a generic scenario where dark radiation, as a result of an interaction, is produced directly by a fraction of the dark matter density effectively decaying into dark radiation. The decay process is controlled by its rate $$Q=\alpha H\rho _{dm}$$ Q = α H ρ dm , where $$\alpha $$ α is the (constant) dimensionless parameter quantifying the strength of the decay mechanism, for the weak coupling between dark matter and dark radiation $$\alpha \ll 1$$ α ≪ 1 . We will solve the field equations numerically by using the statefinder function $$y_{H}$$ y H to appropriately represent the field equation. The F(R) gravity model we consider is described by a nearly $$R^{2}$$ R 2 -model at early epochs and at late-time the model mimic the $$\Lambda $$ Λ -Cold-Dark-Matter model ( $$\Lambda CDM$$ Λ C D M ), and we fine tune the parameters to achieve viability and compatibility with the latest Planck constraints at late-time. Furthermore, we consider the behavior of several well-known statefinder quantities, we find that statefinder diagnostic and Om diagnostic can not only break the degeneracy of different parameter values in the F(R) gravity dark energy model, but also effectively distinguish the difference between the F(R) gravity model and the $$\Lambda CDM$$ Λ C D M model. At last, we compared the theoretical results with the SNIa data.