Is fasting Mondays and Thursdays of every week sufficient to fulfill a vow of fasting three consecutive months (Rajab, Sha'ban, and Ramadan) in the event of inability to complete them due to work circumstances, and is continuity a condition for fasting a vow, or is expiation sufficient if a person is unable to fast?

A Muslim should not make vows (nadhr), for the Prophet, peace and blessings be upon him, forbade vows, as they neither hasten nor delay anything; rather, they are a means of extracting from the miserly. However, if a Muslim makes a vow of obedience to Allah, then it is obligatory to fulfill it, for the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him."

So, whoever vowed to fast Rajab, Sha'ban, and Ramadan, it is obligatory for her to fast them. Ramadan is obligatory by the original sacred law and by the vow, while Rajab and Sha'ban are obligatory by the vow only. If she specified a particular year, she must fast them in that year; otherwise, she may fast Rajab and Sha'ban in any year. Fasting Mondays and Thursdays or feeding the poor does not suffice her as long as she is able to fast, even with difficulty. If her intention was to fast Rajab and Sha'ban consecutively, then it is obligatory to fast them in that manner; otherwise, there is no harm in separating them.