Two things: one your "writings" are subjective. They were based on ideas in a man's head. An opinion, or to be charitable, an educated guess. The best man could come up with until God Himself intervened with His revelation.
Second, no, Islam is NOT "based on" either Judaism or Christianity, even though it hijacks a few of their terms and ideas.
Islam is based SOLELY on the subjective claims of a man who claims to have heard voices in a cave and further claimed they were from an angel of God.
No way for an honest skeptic to evaluate the claim. No eyewitnesses, no supernatural demonstrations of Divine authority.
For all we know, he might have heard voices but they were from an angel of Hell. The evidence seems to point that way.