When I quit cigarettes a year ago, the thought of wanting to smoke another cigarette, I took as not being real and that it will fade away with time. The thought and the urge to have another cigarette did truly fade with time. Do anxious thoughts also fade away with time?
They can do, yes, especially if you treat them the same way ie. not believing they are true, or not believing them to be real.
Anxiety is something that loves to depend on the idea of time however, so if you are looking for anxiety to fade away in time, this kind of thinking may keep it alive a bit longer. But perhaps not.
Anxiety will fade easier with the less need you have for it to be gone. It is a paradox. The moment you no longer argue with it, wish it were different or believe it should be different, then the less it can take a hold. Rather than waiting for anxiety to go, just no longer suffer from it being there. To reduce the suffering, give up your arguments with it. When you fight anxiety, suffering increases. If you give up trying to wrestle with it, although pain may be experienced, suffering is not so prevalent.
Then by itself, anxiety will probably decrease, probably over time.