Fasting on Mondays and Thursdays when he owes expiation for breaking an oath

Praise be to Allah.

Firstly: 

What the Muslim should do is protect his oaths and not swear oaths a great deal or swear oaths except with regard to matters that are deserving of oaths. Allah, may He be exalted, says (interpretation of the meaning): “And protect your oaths (i.e. do not swear much)” [al-Maa’idah 5:89].  

Shaykh as-Sa‘di (may Allah have mercy on him) said in his Tafseer: “And protect your oaths (i.e. do not swear much)” means refrain from swearing by Allah falsely, or swearing oaths frequently, and protect them if you do swear oaths by not breaking them, unless breaking the oath is better. 

Tafseer as-Sa‘di, 1/242 

Secondly: 

The expiation for breaking an oath (kafaarat yameen) is to feed or clothe ten poor persons, or to free a slave. If that is not possible, then one should fast for three days. Allah, may He be exalted, says (interpretation of the meaning):

“Allah will not punish you for what is uninentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masakin (poor persons), on a scale of the average of that with which you feed your own families; or clothe them; or manumit a slave. But whosoever cannot afford (that), then he should fast for three days. That is the expiation for the oaths when you have sworn. And protect your oaths (i.e. do not swear much). Thus Allah make clear to you His Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.) that you may be grateful”

[al-Maa’idah 5:89]. 

It is not permissible for you to move to the option of fasting unless you are unable to do any of the three acts of expiation, namely feeding poor people, clothing them or freeing a slave. 

Ibn al-Mundhir (may Allah have mercy on him)said: 

(The scholars) are unanimously agreed that if a person who swore an oath is able to feed or clothe poor people, or to free a slave, it is not acceptable for him to fast if he breaks his oath. End quote. 

al-Ijmaa‘, p. 157 

Thirdly: 

There is no reason why you should not observe naafil fasts, such as on Mondays and Thursdays and so on, before observing fasts of expiation, or before you have finished all of them, but that is on condition that you do not regard them as part of the expiation. 

But we advise you to hasten to observe the fasts of expiation first, if you are unable to do the things mentioned above with regard to offering expiation for breaking an oath. Hastening to observe the fasts of expiation takes priority because it is obligatory and doing what is obligatory takes precedence over observing naafil fasts. 

And Allah knows best.