Using Mathf.lerp()

lerpexample.cs

class whatever : Monobehaviour
{
	float lerpTimer = 0f;

	void Update()
	{
		if ( /* The lerp is happening */)
		{
			lerpTimer += Time.deltatime;
			alpha = Mathf.lerp(start, end, lerpTimer/duration);
		}
	}
}