I don't know much about aquaponics, aeroponics or fogponics, but I from what I've read on wikipedia I think those require more maintenance and resources than a simple vegetation-covered roof. Therefore I will focus my answer on the latter.
The most low-maintenance, low-resources solution probably is to build a green roof covered with sedum plants. Sedum can survive under many circumstances. In warm climates you may need to water the plants occasionally, but this is not necessary in moderate climates. The only maintenance required is to check your water drains once or twice a year and unclog them if needed. You might want to remove the weeds once every year, but this is not strictly necessary. Basic instructions on how to build a sedum-covered roof can be found here.
Instead of sedum you can grow herbs and/or grasses on your roof, but these require a sturdier roof, more maintenance, more water and possibly also some fertilizer (depending on the types of plants). It's even possible to grow bushes and trees, but you'll need an even stronger roof.