Fonty
Do you mean overcoming the fear of starvation/dying? Or do you mean you already have Anxiety and it is worse during fasting?
The fear of starvation is fairly normal considering we've been brought up to believe we need our three meals a day and daily intake of vitamins and minerals and if we don't get 'em we'll drop dead in two days. The only real way to overcome this internal propaganda is to try fasting out for yourself in shorter spans. Just go for one day without eating first and see how you feel, then a day and a half, two days- three days- five days- one week- two weeks. Once you've fasted for a week or two you will realise that your body is fully capable of fasting safely and the fear of starvation will be a thing of the past.
If you suffer from Anxiety already you may also have to deal with increase attacks during the first few days and you may need to be prepared to face these as best you can but many report improvement in symptoms following fasting of that and other mental illnesses.
Andrew.