One day, I did not get up to perform fajr prayer in its prescribed, fixed time. To atone for my negligence, I said: "It is incumbent upon me to get up with the first azan for the fajr prayer." Is this considered a vow? If it is a vow, then what is the expiation for not fulfilling it?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

If by saying, "It is incumbent upon me to get up with the first Azaan for the Fajr prayer," you mean a commitment that you impose upon yourself to get up in the future, as an atonement for abandoning the prayer on that day, as the question reveals, then this wording signifies an obligation to which you commit yourself, and thus the vow is binding. For the vow to be binding, it is not conditioned to explicitly state the word 'vow'; rather, it is enough to say words that indicate a commitment.

If you intended to commit yourself to always get up at the time of the first Azaan, then you are required to offer expiation for breaking an oath whenever you fail to get up at the time that you have specified. This is similar to the case of a person who swears that whenever he does something an expiation of an oath becomes due upon him. Consequently, expiation is due whenever he does such a thing.

If you did not intend to commit yourself to always get up, then you are required to offer expiation of an oath the first time you fail to get up and then no more expiations are due upon you.

Allaah Knows best.