Airponics
Airponics  was the cultivation of plants without soil by suspending them in an oxygen-rich environment and misting their roots with a nutrient solution.

The Kantare created an airponics bay aboard their stranded ship. It was discovered by Commander Tucker and Sub-Commander T'Pol when they followed a shadow. In this airponics bay, Tucker first met Liana. Later, Liana offered Tucker a fruit from their airponics, the lorella. ()

Kes established an airponics bay on  along with a hydroponics bay to cultivate their own food supply. ()

In 2372, the yields from Voyagers airponics lab were coming out low. ()

In 2375, Ensign Doug Bronowski worked in Voyagers airponics bay. () 

The vegetables in the airponics bay were beamed off the ship when Voyager entered  in 2377. ()

Background information 
The accepted term for the method is . However, "airponics" is the term used in the series. Aeroponics is a very real technology developed in the 20th century.
Botany
Academic disciplines