How can one fulfill a vow to fast as a punishment for not waking up for Fajr prayer, given that one is unable to fast due to fasting throughout the week?

The aforementioned vow is a vow of contention and anger, and its ruling is that of an oath. Its maker is given the choice between fulfilling it or breaking it. In this case, an expiation for breaking an oath becomes obligatory upon him. The expiation for breaking an oath is feeding ten poor persons, or clothing them, or freeing a slave. If one cannot find these, then fasting for three days.

It is not permissible to delay the Fajr prayer beyond its prescribed time without a valid excuse. A sleeping person is excused if he takes the necessary measures to wake up. These measures include: sleeping early, eating less at night, reciting the remembrances before sleep, sleeping in a state of ritual purity (wudu'), and using an alarm clock or seeking assistance from others.