We really have to always use something of repulsion to move. Even moving on a planet, you have a repulsion by your feet/wheels from the ground you're on. Flying in air, you have the body of air what carries and moves you, for any acceleration against friction you again some kind of repulsion.

In space you have no substance thus you need to bring that with you. While on earth you can fly on solar cells virtually for ever, in space even an ion engine powered by solar cells or nulcear force would run out of fuel, because it needs to carry a mass it can push out to move forward (Newton's second law).

Is there really no other way to move in the fabric of space? Would it be somehow even theoretically possible to move just on space itself - like sci-fi engines that bend the space-time to create motion (warp/hyperdrive ect).

What do you think when you play with these thoughts?

Would be great, if we could just create motion mathematically, just by calculating where we would move to...