Per the RAW spellcasting rules, yes. But there are intricacies to consider.
The following excerpts are taking from the PHB, Chapter 10, pages 202-205.
Regarding casting time:
Most spells require a single action to cast . . .
Here we see there are no restrictions on what is happening during a turn, other than the caster needing to spend the appropriate action.
The target of a spell must be within the spell's range . . . once a spell is cast, its effects aren't limited by its range, unless the spell's description says otherwise.
Again, nothing prohibiting positioning, only that the target be in range at the moment the spell is cast.
Verbal: Most spells require the changing of mystic words . . . a character who is gagged or in an area of silence . . . can't cast a spell with a verbal component.
Somatic: Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures . . .
Material: . . . A spellcaster must have a hand free to access a spell's material components - or to hold a spellcasting focus - but it can be the same hand that he or she uses to perform somatic components.
Here, there is nothing RAW stating these cannot be done while falling. However, you as a DM are within your power and reason to determine if components are possible, or only possible with checks, to satisfy the spell's requirements.
For example, somatic components simulate gestures that may be difficult to perform while plummeting toward the ground. It may warrant a Dexterity or Athletics check to pull off against the wind and other forces affecting the caster. Likewise, it might be hard to keep hold of a large staff while spinning wildly in the air. Concentration can be used as a catch-all for the difficulty of the situation.
I haven't personally employed these (I tend to complicate my encounters enough IMO), but I have played at a table where our DM used such techniques sparingly. A particular instance was a vicious storm in which our PCs were described as struggling to even walk upright; the DM had the wizard make a Strength (Athletics) check to be able to hold his arm out with his staff to cast. I agreed with the rationale, and I felt it added a sense of weight and severity to the situation, as well as cause for celebration when the player succeeded. This was the general result we got from whenever the DM employed this technique, in that we felt it added realism and value overall to the story.
Again, none of these are required explicitly in RAW, but are reasonable considerations based on the scenario and what you want your players to accomplish.