Fog Computing offers storage and computational capabilities to the edge devices by reducing the traffic at the fronthaul. A fog environment can be seen as composed by two main classes of devices, Fog Nodes (FNs) and Fog-Access Points (F-APs). At the same time, one of the major advances in 5G systems is decoupling the control and the data planes. With this in mind we are here proposing an optimization technique for a mobile environment where the Device to Device (D2D) communications between FNs act as a control plane for aiding the computational offloading traffic operating on the data plane composed by the FN - F-AP links. Interactions in the FNs layer are used for exchanging the information about the status of the F-AP to be exploited for offloading the computation. With this knowledge, we have considered the mobility of FNs and the F-APs' coverage areas to propose a partial offloading approach where the amount of tasks to be offloaded is estimated while the FNs are still within the coverage of their F-APs. Numerical results show that the proposed approaches allow to achieve performance closer to the ideal case, by reducing the data loss and the delay.