  Ultra-stripped supernovae (USSN) with a relatively low ejecta mass of
$\sim0.1M_\odot$ (e.g., iPTF14gqr and SN2019dge) are considered to originate
from ultra-stripped carbon-oxygen (CO) cores in close binary systems and are
likely to be progenitors of binary neutron stars (BNSs). Here we conduct
long-term simulations of USSNe from ultra-stripped progenitors with various
masses ($1.45\,M_\odot \leq M_\mathrm{CO} \leq 2.0\,M_\odot$) based on results
of neutrino-radiation hydrodynamics simulations, and consistently calculate the
nucleosynthesis and the SN light curves. We find that a USSN from a more
massive progenitor has a larger ejecta mass but a smaller $^{56}$Ni mass mainly
due to the fallback, which leads to the light curve being dimmer and slower. By
comparing the synthetic light curves with the observed ones, we show that
SN2019dge can be solely powered by $^{56}$Ni synthesized during the explosion
of a progenitor with $M_\mathrm{CO} \lesssim 1.6\,M_\odot$ while iPTF14gqr
cannot be explained by the $^{56}$Ni powered model; $\sim 0.05M_\odot$ of
$^{56}$Ni inferred from the light curve fitting is argued to be difficult to
synthesize for ultra-stripped progenitors. We consider fallback accretion onto
and rotation-powered relativistic wind from the newborn NS as alternative
energy sources and show that iPTF14gqr could be powered by a newborn NS with a
magnetic field of $B_p \sim 10^{15}\,\mathrm{G}$ and an initial rotation period
of $P_i \sim 0.1\,\mathrm{s}$.
