Hajj with all its rituals is restricted to the specific places, e.g. Mina, Arafat, etc.

However, one should involve himself in Ibaadat and Dhikr, keeping the greatness of the day in mind. Nabi (Sallallaahu Alayhi Wasallam) mentions in Hadith on the authority of ibn Abaas (Radhiallaahu Anhu) that, "There are no days greater in the sight of Allah and there are no days in which actions are beloved to Allah Ta'ala than 10 days of Dhul Hijjah. Hence, increase in it Tasbeeh (recitation of Subhaanallah), Tahmeed (recitation of Alhamdulillah), Tahleel (recitation of Laa ilaaha illallaah) and Takbeer (recitation of Allaahu Akbar)." (Mutajirur raabih pg.418)

In another Hadith, Hadhrat Abu Hurayra narrates Rasulullah (Sallallaahu Alayhi Wasallam) as saying, "There are no days more beloved to Allah in which He is worshipped than the 10 days of Dhul Hijjah - the fast of each day is equivalent to the fast of a year and standing up in worship of the night of Laylatul Qadr." (Ibid)

The day of Arafat should be spent in condition of fasting and involved in the Dhikr of Allah Ta'ala. Nabi (Sallallaahu Alayhi Wasallam) said, "Fasting on the day of Arafat is a means of wiping off the previous years' as well the coming year's sins." Also Nabi (Sallallaahu Alayhi Wasallam) said, "Fasting on the day of Arafat is equal to fast of 1000 days."

All days of the Islamic calendar, e.g. Eid, Hajj, etc. should be observed as per local calendar. The respective days should be observed according to the sighting of the moon in your area.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai, www.ask-imam.com
FATWA DEPT.