Fog networks have been introduced as a new intermediate computational layer between the cloud layer and the consumer layer in a typical cloud computing model. The fog layer takes advantage of distributed computing through tiny smart devices and access points. To enhance the performance of the fog layer we propose utilization of unused computational resources of surrounding smart devices in the fog layer. However, this will raise security concerns. To tackle this problem, we propose in this paper a novel method using a trust model and Role Based Access Control System to manage dynamically joining mobile fog nodes in a fog computing system. In our approach, the new dynamic nodes are assigned non-critical computing tasks. Their trust level is then evaluated based on the satisfaction rate of assigned tasks which is obtained through different computing parameters. As the result of this evaluation, untrusted nodes are dropped by the fog system and nodes with a higher trust level are given a new role and privileges to access and process categorized data.