Fog-radio access networks (F-RANs) alleviate fronthaul delays for cellular networks as compared to their cloud counterparts. This allows them to be suitable solutions for networks that demand low propagation delays. Namely, they are suitable for millimeter wave (mmWave) operations that suffer from short propagation distances and possess a poor scattering environment (low channel ranks). The F-RAN here is comprised of fog nodes that are collocated with radio remote heads (RRHs) to provide local processing capabilities for mobile station (MS) terminals. These terminals demand various network functions (NFs) that correspond to different service requests. Now, provisioning these NFs on the fog nodes also yields service delays due to the requirement for service migration from the cloud, i.e., offloading to the fog nodes. One solution to reduce this service delay is to provide cached copies of popular NFs in advance. Hence, it is critical to study function popularity and allow for content caching at the F-RAN. This is further a necessity given the limited resources at the fog nodes, thus requiring efficient resource management to enhance network capacity at reduced power and cost penalty. This paper proposes novel solutions that allocate popular NFs on the fog nodes to accelerate services for the terminals, namely, the clustered and distributed caching methods. The two methods are analyzed and compared against the baseline uncached provisioning schemes in terms of service delay, energy consumption, and cost.