Most of the DGX/YPG models, and some of the PSR-E/YPT models, have a Pitch Bend wheel, but they do not have a Modulation wheel.
However, they do respond to MIDI "Modulation" channel messages, and there is a free Yamaha app called Sound Controller for the iPad and iPhone that includes virtual Pitch Bend and Modulation wheels:
Sound Controller adds fun controllers like pitch bend, modulation, X/Y pad and even a MIDI arpeggiator to your compatible and connected Yamaha keyboard.
usa.yamaha.com
Note that the product description says "Connection requires Yamaha i-UX1 interface," but the DGX-505 has a USB TO HOST port so you don't need the i-UX1 interface, just an Apple "Camera Connection Kit" (if your iPad or iPhone has a 30-pin connector) or "Camera Adapter" (if it has a Lightning connector).
If you don't have an iPad or iPhone, you might be able to find a MIDI "controller" app for Android or whatever OS your tablet or smartphone uses, although your ability to connect the DGX-505 to it might depend on whether you can use a USB OTG adapter with it.
Also, the specific type of modulation-- vibrato, tremolo, etc.-- that the MIDI "Modulation" message will add to the voice is dependent on the voice itself, and how it has been programmed by Yamaha.