Pessimists, naysayers and know-it-alls: begone!
To OP: Where are you? Are you interested in at least giving a small ounce of hope in still saving the ship? This will be a tough one, but it's better than just giving up.
Ichigo, listen to Anuranium.
You are almost certainly not going to make it - but there is a tiny sliver of a chance.
If you let people know where exactly you are - and you can't log on to check. They'll need the system, the exact planet, and then you need to pray the planet only has one RES in its rings.
Then it's just faintly possible that someone can go there in Open Play and wait for you. You'd need to log on in Open Play, and then you'll need to luckily log in in the same instance, and within sensor range of the person waiting. That's a throw of the dice, with pretty long odds.
That person then has 19 seconds to target you, deploy a fuel transfer limpet which then needs to reach you and deliver its fuel before your ship blows up.
If all those things happen (very unlikely) then you may be okay by the skin of your teeth.
You'd need to friend whoever it was and coordinate, discussing it in the main menu chat - they'd need to be waiting with the fuel limpet fire group ready and selected and only then could you log on, hoping you're close enough.
Anuranium is one of the Fuel Rats though - I've actually watched the video where he rescued someone far, far out in the deep black of unexplored space. If anyone can do this, Anuranium can.
If it doesn't work, think about what went wrong and how you can avoid it in future. Part of the game is learning from your mistakes:
1. Your ship has fuel; it can run out. Watch your fuel. Plan your routes. Learn how to safely scoop fuel from stars, and which stars you can scoop from (only stellar classes O, B, A, F, G, K and M. Mnemonic to remember: Oh Be A Fine Girl, Kiss Me).
2. Don't go afk in open space. Log off. You don't burn fuel while you're logged off, and it's just a good habit. Also, it can be dangerous logging off near objects like stars and asteroids. Get a little distance from them before logging off.
3. Never, ever fly without your insurance rebuy in your balance. As long as you have your rebuy, you can get back your ship with all its modules for only 5% of its cost if you blow up. If you don't have the insurance rebuy, you can lose everything. Your rebuy amount is shown directly under your balance in your status screen. It's repeated in the financial info.