The earliest accounts have Mohammad and his followers fasting a 10 day period in accordance with pre-Islamic Arabic practice starting on Ashura 10day day of Moharram coniciding with Jewish Yom Kippur ( Bukhar narrating Ibn ‘Umar: The Prophet observed the fast on the 10th of Muharram Ashura, and ordered [Muslims ] to fast on that day, but when the fasting of the month of Ramadan was prescribed, the fasting of the ‘Ashura’ was abandoned. ‘Abdullah did not use to fast on that day unless it coincided with his routine fasting by chance.).
Once the transiton from spiritual leader to warrior leader started in Medina, Islam essentially started to become an Arab state (Jews and others were taxed separately). As national fervor heightened amonst Bedouin Arabs, fasting was extended to the whole month of Ramadan. So there you go as a good Moslem united under the greatest Arab Movement, you must out-fast everyone.
