I know what a desert is however you don't know that historically no one invaded Arabia, as for Africa you are just bringing that up now so that is a different story. Africa was invaded because Muslims were at war with the Byzantines and Byzantines had African holdings such as Egypt, Libya, and Tunis. According to another historian (Will Durant) the rest of Africa was then taken over so as to remove the possibility of a two front war against the Byzantines, so capturing North Africa was entirely for strategic purposes not to mention it is not all deserts like you are making it out to be.