The Muslims managed to expand from the Arabian Peninsula towards the east fairly easily and this was due to the military power, unification, instability in the east, seeking for security and savior of the people in the east.
The Muslim were unified, and that was a very nice example for the people in the east that if they are unified they will be stronger, and they will also have better lives, and be more secure.
The east was divided into multiple smaller countries where there were constant battles and instability, so the Muslims with their unification propagation were seen as saviors. On top of it, the people in the east were desperate for a new savior, a divine figure, and the Muslims brought that to them.