In modern networks, the use of drones as mobile base stations (MBSs) has been discussed for coverage flexibility. However, the realization of drone-based networks raises several issues. One of critical issues is drones are extremely power-hungry. To overcome this, we need to characterize a new type of drones, so-called charging drones, which can deliver energy to MBS drones. Motivated by the fact that the charging drones also need to be charged, we deploy ground-mounted charging towers for delivering energy to the charging drones. We introduce a new energy-efficiency maximization problem, which is partitioned into two independently separable tasks. More specifically, as our first optimization task, two-stage charging matching is proposed due to the inherent nature of our network model, where the first matching aims to schedule between charging towers and charging drones while the second matching solves the scheduling between charging drones and MBS drones. We analyze how to convert the formulation containing non-convex terms to another one only with convex terms. As our second optimization task, each MBS drone conducts energy-aware time-average transmit power allocation minimization subject to stability via Lyapunov optimization. Our solutions enable the MBS drones to extend their lifetimes; in turn, network coverage-time can be extended.INDEX TERMS Cellular network, charging drone, coverage-time, mobile base station, scheduling.