We describe the afterglows of the long gamma-ray-burst (GRB) 130427A within the context of a binary-driven hypernova (BdHN). The afterglows originate from the interaction between a newly born neutron star ($ u$NS), created by an Ic supernova (SN), and a mildly relativistic ejecta of a hypernova (HN). Such a HN in turn results from the impact of the GRB on the original SN Ic. The mildly relativistic expansion velocity of the afterglow ($Gamma sim 3$) is determined, using our model independent approach, from the thermal emission between $196$~s and $461$~s. The power-law in the optical and X-ray bands of the afterglow is shown to arise from the synchrotron emission of relativistic electrons in the expanding magnetized HN ejecta. Two components contribute to the injected energy: the kinetic energy of the mildly relativistic expanding HN and the rotational energy of the fast rotating highly magnetized $ u$NS. We reproduce the afterglow in all wavelengths from the optical ($10^{14}$~Hz) to the X-ray band ($10^{19}$~Hz) over times from $604$~s to $5.18times 10^6$~s relative to the Fermi-GBM trigger. Initially, the emission is dominated by the loss of kinetic energy of the HN component. After $10^5$~s the emission is dominated by the loss of rotational energy of the $ u$NS, for which we adopt an initial rotation period of $2$~ms and a dipole plus quadrupole magnetic field of $lesssim ! 7times 10^{12}$~G or $sim ! 10^{14}$~G. This scenario with a progenitor composed of a CO$_{rm core}$ and a NS companion differs from the traditional ultra-relativistic-jetted treatments of the afterglows originating from a single black hole.
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