  In this paper, we first extract general uncharged accelerating BTZ black hole
solutions and study some of their properties. Our analysis shows that
spacetime's asymptotic behavior depends on four parameters: the cosmological
constant, mass, acceleration, and topological constant. Then, we study the
temperature of these black holes and find that the temperature is always
positive for AdS spacetime. Next, we extend our study for extracting charged
accelerating BTZ black hole solutions in the presence of a nonlinear
electrodynamics field known as conformally invariant Maxwell. Our findings
indicate a coupling between the electrical charge and other quantities of the
accelerating BTZ black holes. The asymptotic behavior of charged accelerating
BTZ black holes depends on five parameters: the cosmological constant, the
electrical charge, mass, the acceleration parameter, and the topological
constant. Then, we studied the effects of charge, acceleration parameters, and
the topological constant on the root of these black holes. Finally, we
investigate the temperature of these black holes in AdS spacetime. For these
black holes, the temperature depends on the electrical charge, accelerating
parameter, and the cosmological constant. Our analysis indicates that the
temperature of charged accelerating BTZ AdS black holes is always positive.
