This is a phobia that is characterized by an extreme fear of growing old. People with gerascophobia may experience intense anxiety and fear when thinking about aging, or when confronted with the physical and mental changes that come with age. Symptoms may include panic attacks, avoidance of activities related to aging
From Wikipedia
Gerascophobia is an abnormal or incessant fear of growing older or ageing (senescence). Fear is characterised as an unpleasant emotion experienced as a result of some perceived threat or source of danger, in the case of gerascophobia that threat is ageing. This fear is irrational and disproportionate to any threat posed and persists even in the case that the individual is in perfect health.