Space-time duality for fractional diffusion

Understand

Zolotarev proved a duality result that relates stable densities with different indices.

• In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion.
• Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives.
• They govern scaling limits of random walk models, with power law jumps leading to fractional derivatives in space, and power law waiting times between the jumps leading to fractional derivatives in time.