Is it permissible to combine the intention of fasting the White Days with the intention of fasting to expiate an oath?

If the fasting days for expiation of an oath coincide with the Ayyam al-Beed (the White Days), it is hoped that one will attain both rewards: absolution from the expiation and the reward for fasting the Ayyam al-Beed. Jurists have stipulated that if someone fasts to make up for missed Ramadan days, for instance, on the Day of Ashura, it is hoped that they will receive both rewards. Al-Khatib al-Shirbini stated that the reward for fasting the Ayyam al-Beed is attained by whoever fasts them, even if without the intention of voluntary fasting, because the objective is simply to fast on these days. It is better to intend the obligatory fast, and the reward for the supererogatory fast will be attained, God willing.