Mars has the largest and most violent dust storms in our solar system.

Martian storms can last for weeks or even months! The winds there can blow dust for up to 60-100 mph. The energy of the dust storms come from the sun. Dust storms begin after Mars is closest to the sun. Mars has much worse dust storms than Earth because it doesn't have any oceans or water in the atmosphere.

For the science behind it, NASA can explain it in more detail.