Is expiation (kaffarah) obligatory for someone who vowed to fast two non-consecutive months, then was accepted into university and fasted part of the period, then stopped fasting due to circumstances, and the days she recorded as fasted were lost, and there remained an unknown number of days for certain, so she fasted 8 of them, and 12 days remained, but she doubts the correctness of this number? And is it necessary for her to fast the remaining days to fulfill her vow?

A conditional vow must be fulfilled if the condition is met. There is no requirement for consecutive fasting when fulfilling a vow, and no expiation is due for breaking the sequence. The remaining days of the vow must be made up. If the exact number of days is unknown, one should investigate and strive to make up the number of days that would clear their conscience with certainty or a strong presumption. Whoever vows an act of obedience to Allah must perform it. It is not permissible to break such a vow unless one is unable to fulfill it, in which case an expiation for breaking an oath (kaffarat yamin (definition)) is required. Vows are disliked and do not alter Allah's decree. The Prophet (peace be upon him) said regarding vows: "Indeed, a vow brings no good; it is only used to extract from the miser."