An Excerpt from  Minhaj Et Talibin (A Manual of Muhammadan Law) Imam Nawawi 

BOOK 6._FASTING

CHAPTER 1._GENERAL PROVISIONS
SECTION 1 -

THE fast of the month of Ramadan becomes obligatory, ‘i.e. commences, either upon the termination of the thirty days of the preceding month of Shaban, or from the first appearance of the new moon. The testimony of a single irreproachable witness—or of two, according to one authority —is sufficient to establish the fact of this appearance. lf there be only one, he must unite all the  requisites of an ocular and unexceptionable witness; so that the testimony of a slave or a woman cannot be accepted..
If the fast has been begun on the testimony of a single irreproachable individual, but the moon is not seen for the next thirty days, the fast must still be terminated after that period, even though the sky may have been cloudless. A sight f the moon in any place renders  obligatory the commencement of the fast in that neighbourhood, but not  in places situated at a great distance. By great distance is understood a distance which permits of the abridgment of prayer, or, according to others, a distance that causes an appreciable difference in the rising of the heavenly bodies. [The latter opinion is the better.]
When, by reason of the above rules, the fast is not yet obligatory  in a certain place, a traveller, arriving from a place where the moon has already been seen, should conform to the local observance. And he should act in the same way on arrival at a. place where the moon has already been seen, coming from one where it has not yet been observed. But if in this way on arrival at a place he celebrates with the inhabitants the feast at the end of the fasting month, he must make up afterwards for the day’s fasting he has thus omitted. A passenger on a ship leaving on. the morning of the . feast and arriving the same day at a distant place where the inhabitants have not yet terminated the fast, should conform to the local observance during the rest of the day.
 

Mahyuddin Abu Zakaria Yahya ibn Sharif an-Nawawi, Minhaj Et Talibin  [Minhaj al-Talibin],   trans. by L.W.C. van den Berg into French and thence by E.C. Howard into English, London, 1914: book 6, sections 1 .