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Anecdotally, I'd like to add that I run much better fasted than not. Granted I only run for 30 to 60 min, but even up to 36 hours fasting did not make it harder at all. I feel lighter, euphoric and my motivation does not change over the time running.

Though, I speculate that running in the beginning of your fasting window will increase the time of glucose depletion and maaaybe make the fasting more efficient. Though, repairing exercise induced injuries probably won't be efficient.