In this paper we introduce the Starting-Energy Fair Queuing (SEFQ), a novel class of energy-aware scheduling algorithms aim to guarantee a target lifetime to mobile devices while providing proportional energy consumption and time-constraint meeting to tasks. With the extension of fair queuing to the energy domain, energy consumption of CPU is managed in a way that each task is guaranteed a share of the average power of a fixed period. The simulation results show that the performance of time-sensitive tasks can be traded-off with their fairness.