Some Random Directions in Fractional Derivatives Vaughan Voller Work with Chris Paola. Efi Foufoula, Vamsi Ganti and Dam Zielinski The objective of this talk is to present two recent excursions into solving problems with fractional derivatives. The first topic—introduced briefly at the pervious STRESS meeting—will outline how a random-walk solution for fractional diffusion equations can be generated using what we refer to as a "random domain shifting" technique. The second topic looks at non-local model of sediment transport in the source—to –sink long profile. Form previous STRESS related meetings it is observed that models of upland erosional systems use fractional diffusion treatments with a non-local direction only directed upstream, whereas models of depositional systems employ a downstream only non-local direction. With a simple long profile model, it will be demonstrated here, that physical realistic solutions for the fluvial surface shape can only be predicted if this bifurcation between erosional and depositional systems is enforced. A discussion of why this might be true and its possible consequences for fractional derivative models of non-locality in land-scape dynamics will be discussed.