Having seen the crescent himself, but was unable to inform Sharee'ah court
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Question: If a person has ascertained the beginning of the month by having seen the crescent, but was unable to inform the Sharee'ah court, is he obligated to fast?

Response: The scholars have differed over this issue. Some of them say he must fast, based on (the fact that) the actual crescent is what is well-known amongst the people, or that it was seen after sunset, regardless of whether it was widespread amongst the people or not.

And that which appears to me is that the one who sees it and is certain that he has seen it, and he is in a far away place such that no one else saw it with him, then he must fast. This is based on the generality of the verse:
{So whoever amongst you see the month (i.e., the crescent) then let him fast it}, [Soorah al-Baqarah, Aayah 185], and (also) the saying of the Prophet (sal-Allaahu `alayhe wa sallam):
((If you see it (the crescent), then fast…)).

However, if he was in a city, and he testified to having seen the crescent at the Islaamic court, but his testimony was rejected, then in this case he should fast in secret, so that his differing with the people is not publicised.

Shaykh Ibn 'Uthaymeen
Fataawa Ramadhaan - Volume 1, Page 59, Fatwa No.26;
al-Fataawa libni al-'Uthaymeen, Kitaab ad-Da'wah - Volume 1, Page 149