In fog computing, processing, network, and storage resources are placed close to the end users to assure a low latency in comparison to the latency experienced when accessing services in the cloud. One limitation of this solution, however, is that fog nodes are usually fixed, whereas demands are variable over time at all locations, resulting in underutilization of the fog resources as well as unnecessary provisioning of fog resources. One way for dealing with this problem is the employment of mobile nodes to cope with the variability in resource demand. This paper studies how unmanned aerial vehicles (UAVs) equipped with processing capabilities can be used in this perspective, and proposes a solution to the fog node location problem considering both fixed and mobile nodes. It proposes the UAV Fog Node Location (UFL) algorithm to evaluate potential replacements of fixed servers by UAVs. The proposed algorithm can be used for long term planning under the assumption of changes in the prices of UAVs. An evaluation of the problem using data generated by real mobile users shows that UAVs can improve the design of future fog networks. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.