Before the release, we might have been applying the force but just after the release we are not applying any force, the ball has inherited the motion of the hands, and it is having its own velocity.
Now why to take the gravity, to know about the behavior we should go special instead of going through complicated situations.
So, after initial velocity, the air resists it let for 'dt' time, then its velocity decreases, now in again another 'dt' time it encounters with less no. Of air particles which can be calculated by the product of its velocity at that instant and dt time.
This way we conclude to the formulae
M. (dv/dt) = - k. v = - k. (ds/dt)
Where k depends on quality of air., density of air.