Is it permissible to divide prayer times according to when the worshiper wakes up at night, or is there another solution to the problem of accumulating obligatory prayers resulting from varying sleep and wake times?

Prayer before the age of discernment is not considered [valid], and after it, a Muslim is rewarded for it. After puberty, prayer becomes obligatory, and whoever abandons it or intentionally delays it past its prescribed time incurs sin. The prayer times are fixed and cannot be altered. If a Muslim sleeps before the prayer time begins and wakes up after it has ended, there is no sin upon him, and he must pray immediately upon waking, while also taking measures to ensure he wakes up. If he misses prayers due to sleep, he must make them up immediately, observing their proper sequence, unless he fears missing the current prayer. Changing the prayer times is not permissible.