  Black hole perturbation theory is a useful approach to study interactions
between black holes and fundamental fields. A particular class of black hole
solutions arising out of modification of Einstein's general theory of
relativity are regular black holes (RBHs) which can be constructed using a
nonlinear electrodynamic Lagrangian. Because of their importance, we are
interested in studying the behavior of three kinds of such RBHs under
perturbations generated by an external field. Indeed, we investigate the
quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs
which is non-minimally coupled to the Ricci scalar tensor of background
geometry. We will attempt to find the low-lying quasinormal frequencies of the
perturbations by using WKB approximation. We shall also study the relationship
between the QNMs and some characteristic properties of black holes such as
grey-body factors, area quantization, and shadow radius.
