You can animate visibility of object, or link it by expression to something like scale, let's say if scale is smaller than some value, visibility is zero. Or, to use ICE instances and just delete the particles. However this is Boolean, on - off, nothing in between. Same behavior as in Maya or Max, if I'm correct. Also it worth to checkout, how this works with particular renderer, especially in case of motion blur.
For small example, while ago in one early version of 3delight I had to move particles across one frame, away from camera, exactly along camera ray, behind matte plane, to avoid the motion trail to 'nowhere', when they were deleted. Not hard task for ICE, anyway.
Gradual transparency by object, this belongs to material in SI, Maya, Max and Houdini (if I'm correct....). Perhaps the most versatile method in SI is, again, ICE instance, where transparency is driven by ICE attribute.
The renderer "turtle" used by this scene, is not currently available. The "turtle" renderer will be used instead.