  We investigate the bound orbits of massive/massless, neutral particles and
photons moving around regular black holes of Fan and Wang. For massive
particles, we show the existence of stable/unstable circular orbits and the
charge dependence of the radius of the innermost stable circular orbit.
Remarkably, we find an unstable circular orbit of photons inside the event
horizon. For massless particles and photons, we show that both stable and
unstable circular orbits can exist in a regular and horizonless spacetime with
a slight overcharge. Then, we also discuss the periapsis shift of massive
neutral particles orbiting around the black hole, and show that the charge
gives a negative correction to the shift for black holes with small
nonlinearity of electrodynamics.
