In order to promote the value circulation of energy resources and improve energy efficiency, credible energy sharing between Internet of Things Devices (IoTDs) came into being. However, sometimes IoTDs do not obtain the required energy in the required time period, resulting in less active participation in energy sharing. To address these challenges, this paper first proposes a credible energy transaction model based on the distributed ledger blockchain at the Edge of the Internet of Things, where the Edge Cloud Server (ECS) can collect a large number of surplus energy resources of IoTDs in a secure and credible energy sharing environment and share them with other IoTDs in urgent need of charging. Meanwhile, in order to attract IoTDs to participate in energy sharing for a long time and meet the energy demand of ECS to the maximum extent, a smart contract-based Expected Social Welfare Maximized double auction incentive mechanism of Single ECS to Multi-IoTDs (ESWM-StM) is proposed to enable dynamic and adaptive energy sharing from multiple IoTDs to a single ECS. In addition, this paper compares the proposed algorithm with the benchmark method in terms of energy-sharing cost and long-term utility. The simulation results show that the proposed incentive mechanism can enable IoTDs to provide more surplus energy per unit cost to meet the energy demand of ECSs, and can sustainably attract more energy trading participants to enhance the expected social welfare in the long term.