If anxiety is caused by a phobia, which is defined as an unreasonable fear, how does one handle thanatophobia, and control anxiety caused by it?

We all have some: Fear of death and need to cope with the inevitability that life will end. If you are 39 and healthy, it has become irrational or all encompassing and therefore it is a phobia. Psychotherapy is the best way to handle it.

Thanatophobia: (From Greek:Thanatos meaning "death" and Phobos meaning "fear") is an intense and irrational fear of death. While it sounds normal to be afraid of dying, people with it responds to this knowledge in excess. They feel queasy whenever they sense any danger, not only for themselves but for their family and friends. The extreme fear makes them feel stressed and unproductive.

It’s best to have a physical exam to know if you have an illness. If not, you could see a Clinical Psychologist with expertise in multiple types of psychotherapy for help with your anxiety and, if needed, a Psychiatrist for medication.