I wanted to travel in the morning and I made an intention to fast, but at the time of Dhur I felt some difficulty, is it permissible for me to break the fast; and if I break the fast, what is the expiation for that?
There is no harm to break your fast if you are travelling, even if you did make an intention to fast. As long as you have left the country, (or the boundaries of your city), it is permissible for you to break the fast; rather it is better (to break the fast). As for if you are in the country (or within the boundaries of your city) and you have not travelled yet, it is impermissible (to break the fast), and it is impermissible for you to break the fast as long as you are in the country (or within the boundaries of your city).
But for example, you are to travel tomorrow and at present you have made an intention to fast and then you travelled, it is permissible for you to break the fast whether you encounter difficulty or not, and expiation is not incumbent upon you.
As for if you intended to travel and made an intention to fast, but you did not get to travel and you broke your fasting when Dhur came, then you are forbidden to do this and you have committed a crime. It is incumbent upon you to repent and repay that day’s fast. However, if breaking the fast was done after you (started) travel, then there is no harm (in this) Inshaa-Allaah.
[For further deatils, see: Al-Fataawaa Wad-Duroos Fil-Masjidil Haraam of Shaikh Abdullaah Bin Muhammad Bin Humaid (rahimahullaah) pages: 485-486]