Fractional transport equations for Levy stable processes

The influence functional method of Feynman and Vernon is used to obtain a q uantum master equation for a system subjected to a Levy stable random force . The corresponding classical transport equations for the Wigner function a re then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the S moluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equat ions recently proposed are clarified.