Here are some tips from flight attendants for fighting the exhaustion...
Stay awake until a normal bedtime, and don’t sleep in. You’ll adjust to the new time zone faster if you get on schedule that first night.
Put your feet up as soon as possible. All that sitting on the plane can make your legs and feet swell up. Prop your feet up for five to ten minutes.
Load up on carbs. Keeping your insulin levels up can help your body adjust to a new schedule.
Get some exercise or some fresh air. Even just a walk around the block can help you sleep better and adjust to a new time zone faster.