What is your death to you, that it can frighten you?
Fear of death is a rather diffuse fear, and you'll find it tends to be elusive when you reflect and try to get a grip on it. Being dead is not like an experience (at least none that we can know of, or could have had any previous encounters with); it's not possible to imagine what it is like. And that's not because it is an experience that's so incredibly dreadful, but because it isn't an experience at all. When you're dead, you are no longer there to experience anything, and thus there is no such thing as you, experiencing whatever it may be like to be death. You can of course imagine a pitch-black darkness, accompanied by deep silence. But what you'd imagine here would still be you, as experiencing a situation in which there is no input to the senses — but not a situation in which you're no longer there. You can't imagine being dead, because there is no experience here to present to the imagination.
Sometimes what people imagine when they are afraid is not so much death itself, but the process of dying; they might imagine it as painful, or as involving inabilities for long periods. Another worry might concern the dignity they hope to be capable of during their last moments; this is often more about the perceptions of others than about themselves. These sorts of fear aren't quite as intangible as fear of death, but they're of a different sort, and we'll deal with them some other time.
Likewise, you can of course imagine how the life of others, such as your friends and children, might look like once you're gone, how they will live on without you. You can fear the impact that your death will have on the life of others, and that's indeed a deeper point: certainly the well-being of at least some people around you should be a matter important to you. And obviously, this significance lasts longer than merely to the end of your life's time. (Whereas your own sorrow and pain does end at that point.) In fact, most of us make some provisions for those we love exactly because we envisage the possibility we might not be around at all those future times when they might come into some need.
However, while it is a valid concern to some extent, we must also consider that as a matter of fact life will go on for all those we leave behind. In most cases at least, they will eventually recover from their loss. (And this is also what we should wish for them, unflattering for ourselves though it may be. If a person can never go on with their life after the loss of someone, however close they may have been, that shows something deeply problematic about the relationship that's been between them: it would look more like one of dependence and needfulness rather than one between people in full possession of their own integrity as a person.)
Another fear is that of an unusually early death, one at a time that marks perhaps only the middle of the average life time of the people around you. The sources of this fear are sometimes obviously questionable or outright foolish (such as jealousy: are others better than I am, so that fate lets them live longer? — or a kind of greed: wouldn't I've been able to travel to even more interesting locations, or could I've enjoyed more good food and wine if I'd lived twice as long?) In other cases, what disturbs those with this kind of fear rather is the thought that some of their important projects will be spoiled: they won't be able to complete some work that is most dear to them. This thought, though it's a worthier worry, still betrays a mild confusion. It has been clear and certain all along that death may catch you early, forcefully ending some projects you hoped you'd be able to complete; it's an ever-present possibility that you may fail to achieve some of the goals you think of as important. That's not of course a reason to refrain from taking on these goals at all; yet there has never been a guarantee that you would reach them, and if, in the end, you don't, that is not a basis for justified disappointment. If there's disappointment, then it comes from some false hope which you adopted in the course of pursuing your projects.
If you've come to make a project of such a sort a life-defining project, then you've chosen a project of the wrong sort. A proper life-defining project, a project that results in making your life a good one, can't rely on the assumption that your life will last a certain minimum amount of time (an assumption which cannot be guaranteed).
Death can happen at any time, in any one of many different ways. But even if it puts an end to a good life, the mere fact of its ending doesn't make that life less good. How could it? Every life has to end at some time, and when that time is will be arbitrary. Goodness of life is a quality, not a quantity. A life is good because of how well it's lived, not because of how long it continues. Take care.