I have a 2862 installed at my office and each day when an iPhone user connects (which happens to be the boss's :x) the phone shows as connected to the WIFI but then keeps swapping between the 5GHz and the 2.4GHz.
There isn't much distance between the router and the phone but there are glazed partition walls.

Is there a way to bind the device to only one frequency using the white and black lists?

If your area has radar signals that the router can detect, that can definitely cause the kinds of problems you're seeing.

Try to use just channels 36, 40, 44 & 48, those are non-DFS channels that can be used even with radar signals and won't need to take the radio offline to do DFS detection. If you do use DFS channels and the router detects radar frequencies on the channel(s) it's using, it will switch to another channel.
You can force the DFS channels to a certain extent by setting the Channel to Auto mode and selecting the allowed channels in the [Advanced Settings] menu with the "Auto Channel Filtered Out List" tickboxes - is that showing on your 2862? I'm not seeing that option on the one I'm accessing right now.
I can see the option in the Vigor 2860ac's menus.

Thanks admin 3, we have a lot of RF and Bluetooth but no radar.
I've set the channel to 40 now to see if this helps. Believe a power saving mode in the iPhone has been a red herring to why the pings have been intermittent.
No sign of the advanced channel for filtering the out list on our 2862 unfortunately.

This is annoying me. See my posts under topic 21981

Annoyingly my 910c allows the 5ghz dfs to be fixed and not change.

my 902 keeps changing channels onto frequencies used by neighbors.

most recent firmware 902 can switch to channel that is checked in the black list to not use.

Annoying...