No, the only Muslims that came that far were Turks. They did not attack Byzantium until 1453. That was the first attempt to advance and the city fell.
Byzantine Empire
Just fine, the empire existed for many centuries.
The Seljuks or the Sufi's
The Ottoman Empire, but truthfully due to a series of civil wars and partial defeats by other empires the Byzantine empire had been in decline for centuries prior to their final defeat
the byzantine empire ended when the Ottoman Turks invaded Constantinople in the year 1453 A.D. The Turks kept the name Constantinople for centuries, but renamed it Istanbul in 1930.
The Byzantine Empire was the old Eastern Roman Empire, which lasted much longer than the Western Roman Empire. Eastern Orthodox Christianity became the dominant religion for a while in the East, while Roman Catholicism dominated in the West. The Byzantine Empire eventually fell to Muslim invaders.
The Byzantine Empire had been growing steadily smaller and weaker for centuries, but it was finally defeated altogether by the Ottoman Turks in 1453.
Justinian Code
The Eastern Roman Empire was not affected by the Germanic invasions which precipitated the fall of the west. The Eastern Roman Empire continued to exist for another 1000 years, even though it lost many of its territories to Arab, Slav and Turkish invaders over the centuries. Historian call the Eastern Roman Empire after the fall of the Western Roman Empire the Byzantine Empire.
The Bulgarians and the Arabs were the 2 main enemies of the byzantine empire.
The Gupta Empire ended when Chandra Gupta II died and waves of invaders moved into India and broken the Gupta Empire into several smaller kingdoms.
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