Violation Or Not
 

A1 dribble, stop to throw a pass to A2. A2 does not see the pass so A1 runs to get the ball. Now A1 cannot dribble again, but can A1 pick up the ball and pass.

Because A1 has already used his dribble, it would be a violation for him to recover the errant pass. The pass (since it was not touched by another player) is considered to be a second dribble. When A1 touches the second dribble, it's a violation for an illegal dribble.

Violation as Scrap explained. Just want to throw this out there, no pun intended. If A1 starts to throw a pass and sees A2 vacate where he intended to pass, and stops and pulls the ball back and in the meantime, fumbles it away from himself, he can retrieve the ball.

OK Then why does it said that it is a illegal dribble to pickup a fumble that has not been touched or been touched by, another player. rulr 9.5.3

Rule 9-5-3 does not say that it's an illegal dribble to pick up a fumble after a dribble. Picking up the fumble is legal. Dribbling again <b>after</b> picking up the fumble isn't. That's what the rule is stating.