It depends on the Rightly-Guided Caliph in question.
Abu Bakr and 'Ali (first and fourth caliphs) dealt with internal civil wars, so they were not primarily responsible for the expansion of the Islamic Caliphate. However, 'Omar and 'Othman (second and third caliphs) did fight numerous expansionary wars, throughout the Levant, Mesopotamia, Persia, and Egypt.
It depends on whether you consider western Anatolia to be part of Southwest Asia. The Rightly-Guided Caliphs conquered all other regions of Southwest Asia, including Arabia, Egypt, the Levant, Mesopotamia, Persia, and eastern Anatolia. However, Muslims under the Rightly-Guided Caliphs left western Anatolia under Byzantine control.
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Two changes that the Rightly Guided Caliphs made during their rule was the institution of consultation and meetings of the council.
Umayyads
Madinah
The Umayyads and the Abbasids.
The rightly guided caliphs
The Umayyad Caliphate came after the four Rightly-Guided Caliphs.
Almost All. With the exception of Anatolia, which some people consider to be outside of Southwest Asia, the Rightly-Guided Caliphs united all of Southwest Asia.
There were FOUR Rightly-Guided Caliphs after Muhammad's death (Abu Bakr, Omar, Othman, and Ali). After Ali was assassinated, the Umayyads swept into power, ending the age of the Rightly-Guided Caliphs and beginning a more imperial form of government.
Having the power and leading the Muslims and receiving the huge tax and governmental income from 2/3 of the world. The Rightly-Guided Caliphs further extended the Islamic Empire and created state structures to more effectively manage the conquered regions.
They used Muhammad's actions as guides to leadership.