Slider movement = animation speed

I am using a custom made UI slider that is used to limit the speed at which the slider can be moved. The issue I am having is that when I move the slider the movement isn't smooth. The slider is used to scrub through an animation and it needs to moved smoothly and slowly. So far the speed at which the slider can be moved has been limited, however when the slider is moved it isn't smooth. How do I smooth the movement of the slider?