The problem of capturing a target in the presence of obstacles, studied through the prism of viability theory, has been the topic of many studies. The capture basin algorithm, which generalizes to target capture problems the original viability kernel algorithm, allowed on one hand to determine capture basins and reachable sets and, on the other hand, to compute value functions (minimal time-to-reach, survival or exit time functions ... ) while revealing viable feedbacks or optimal control rules. In the case of mobile targets, although the introduction of the running time as a 'true' state variable allows to define extended capturability or reachability concepts, we need to define capture concepts other than the minimal time or other optimal one. Applications to moving target capture problems are numerous. We present two examples, one dealing with the research of defense strategies to face multiple mobile threats, the other with repositioning strategies for a fleet of autonomous electric vehicles requiring energy refill at different fixed terminals available.