Fear is an integral part of life and tends to increase with age but it is only a symptom and not the disease. Vedanta has analyzed it and says: ‘Fear arises at the empirical level from our attachments, our likes and dislikes’.
We fear that we will get what we dislike and loose what we like. For example diseases and the loss of life or wealth. Fear arises, as we want to hold on to things we are attached to and what we like. But the world is ever changing and transient.
The fear of losing all what one values and of getting afflicted by disease increases with age. A person who is free from attachments is unaffected by this. Bhartrhari says dispassion alone makes one fearless.
The subtlest cause of fear is alienation and the sense of otherness. There is no fear of oneself. Fear always arises from another. One who sees the Self in all is truly fearless.
Source - You Ask He Answers By Swami Tejomayananda