I made a vow that if I became able to do something to help some of my acquaintances, I would fast some days for the sake of Allah, the Exalted. I had something in mind while making that vow, but I cannot remember whether I stated it in the vow or depended on the fact that Allah, the Exalted, already knew it and that there thus was no need to mention it. If I do something to help those people that is different from what I first intended but leads to the same result, i.e. helping them out, will I still be required to fulfil my vow?

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 is His slave and Messenger.

When one renders his vow conditional on the occurrence of a particular thing, then he is obliged to fulfill his vow when that particular thing takes place. ‘Aa’ishah reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to do an act of obedience to Allaah, the Exalted, must do it…" [Al-Bukhari] The vow-taker's intention is the essential factor that limits the (broad implications of) a vow, as it restricts the general indication of the vow's words and specifies what is absolute thereof. The Prophet, sallallaahu ‘alayhi wa sallam, said: "The (reward of) deeds depends upon the intentions, and every person will receive the reward according to what he has intended." [Al-Bukhari and Muslim]

Hence, if one vows to do such-and-such action whereby a person draws close to Allaah, the Exalted, if he becomes able to help certain people in a specific way, then it becomes incumbent upon him to fulfill his vow once he becomes able to do so.

As for your case, the ruling depends on your intention while making the vow. If you intended to help those people only in the way that you had specified, apart from any other way, then you are not obliged to fulfill such a vow unless you become able to help them in the way that you vowed. However, if your intention was to help them in any possible way, without specification, and you only specified that act or way of help because you thought it to be the most appropriate in your opinion, then you are obliged to fulfill your vow. A well-established rule in the Sharee'ah, upon which almost all scholars agree, is that matters are to be judged based on the intentions.

Allaah Knows best.