Must a vow to fast for a week be fulfilled if the desired outcome is not fully achieved?

A vow conditional on a disliked condition is disfavored, yet it must be fulfilled if the condition is met, based on the Almighty’s saying: {And let them fulfill their vows}, and the Prophet’s (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him."

If the condition is not met, nothing is binding, and fasting in that case becomes supererogatory.

What is binding from the vow is determined by the intention and purpose of the one making the vow at the time of making it. If he intended the complete fulfillment of the vow, then fasting is not binding upon him until its entirety is fulfilled. If he intended the fulfillment of part of it, then fulfillment becomes binding upon him when that part is fulfilled; because a vow is based on intention.