Dear Khalid -- You might try testing dates against the Islamic calendar
using calendar.el's functions. e.g. using org-mode diary-sexp syntax:

* Holy Month
%%(equal (seq-take (calendar-islamic-from-absolute (org-today)) 2) '(9 1)) 
Start of Ramadan

I did try this just now, but it doesn't seem to make the "start of
Ramadan" entry on February 18. Maybe someone else can help more.

> Can I track Org habits with an alternate calendar instead of Gregorian,
> such as Islamic calendar?

I'm not sure how org habits work with diary-sexps.

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