Is expiation required for one who vowed to fast Mondays and Thursdays, then broke some days due to an excuse?

A Muslim must fulfill his vow in the manner in which he made it, in compliance with the words of Allah Almighty: "And let them fulfill their vows." If a specific vow cannot be fulfilled due to inability, such as illness or forgetfulness, then there is no expiation or make-up for it. However, if the vow is broken without a valid excuse, then it must be made up.