Ramadan began when he was in another country but he did not fast with them because he was travelling. Does he have to make up that fast?
Question

I am Egyptian and I went on a trip to Turkey one day before Ramadan. The following day, when I arrived in Turkey, it was Ramadan for them, but not in Egypt, i.e., the new moon of Ramadan was seen in Egypt one day after Turkey. So I did not fast on the first day of Ramadan there, because the holy month had not yet begun in Egypt, and I started to fast with Egypt. I stayed there for five days, and I completed Ramadan with thirty days. Is my not fasting on that day correct, on the basis that I was travelling? It was the second day after my arrival there, and I was extremely exhausted because I had spent an entire day looking for a hotel. Do I have to make up that day, or do I not have to make up that day because I completed thirty days of Ramadan, or do I have to make it up and offer expiation because I deliberately did not fast?
Praise be to Allah.The basic principle with regard to one who stays in a country is that he should fast with the people of that country and break the fast with them, and it is not permissible to differ from them with regard to the beginning and end of the fast. 
This has been discussed in the answers to questions no. 106491 and 71203
But because you were travelling at the time when Ramadan began, there is no blame on you for not fasting, based on the concession that allows the traveller not to fast. 
But you have to make up that day that you did not fast, because fasting it was obligatory for you in that country. The fact that you completed thirty days of Ramadan in your country does not mean that the obligation to make it up is waived in your case, because when you fasted the thirtieth day, you did not intend to make up the day when you did not fast. 
We put this question to Shaykh ‘Abd ar-Rahmaan al-Barraak (may Allah preserve him) and he ruled that you must make up the fast. 
See also the answer to question no. 93432 
And Allah knows best.