The Barrow holographic dark energy (BHDE) framework arises from Barrow entropy \cite{ Phys. Rev. D 102 (2020) 123525, Phys. Lett. B 808 (2020) 135643 }, which incorporates possible fractal deformations of the horizon surface and is characterized by the Barrow exponent Δ, thereby modifying the standard holographic dark energy scenario. We have studied the effect of dynamical radiation in the interacting Barrow holographic dark energy (BHDE) model for a non-flat universe. For both open and closed universes (“open” and “closed” refer explicitly to the sign of the spatial curvature parameter $k$ present in the FLRW metric ), we derived the evolution equations for the energy density parameters of dark energy, dark matter, and radiation by considering four different types of interactions among the other possible linear phenomenological forms. These coupled differential equations were then solved numerically to examine their behavior with respect to the redshift parameter. The variation of the dark energy equation-of-state parameter with redshift was also explored for the different interaction models. For all four interaction cases, we found that higher values of the Barrow exponent lead to a transition of the dark energy equation-of-state parameter from the quintessence region to the phantom region at late times, corresponding to lower redshift values. We also identified distinct epochs corresponding to dark energy–dark matter, dark energy–radiation, and dark matter–radiation crossings.

Using data from the Cosmic Chronometer, Baryon Acoustic Oscillation, and Pantheon+ samples, we constrained several cosmological parameters of the interacting BHDE model. The estimated Hubble parameter values in our model are higher than those predicted by the ΛCDM model. This result suggests that our framework could provide useful insights for future studies involving high-redshift data and may contribute to resolving the Hubble tension problem. A statistical comparison between our models and the ΛCDM model has also been carried out.