Al Allaamah Ash Shaykh Saalih Al Fawzan (Hafidahullah) was asked: Is it obligatory to have the intention for all fasts whether they are supererogatory or in Ramadan?

It is obligatory to have the intention for the supererogatory or obligatory fasts. The Messenger said “Verily actions are based upon the intention”. For the obligatory fast it is a must that the intention is made prior to the coming of Fajr. As for the supererogatory fasts it is possible for a person to keep the fast after the coming of Fajr, if he has not eaten or drank after Fajr. It is therefore permissible to make the intention for the supererogatory fast during the day because (the affair) is broader for supererogatory fasts.

Reference: http://alfawzan.af.org.sa/node/15568