A fractional diffusion equation which was based upon Riemann-Liouville fractional derivatives was solved exactly, with the initial values being given as fractional integrals. The solution was obtained in terms of H-functions. It differed from known solutions, of fractional diffusion equations, which were based upon fractional integrals. The solution of fractional diffusion based upon a Riemann-Liouville fractional time derivative did not have a probabilistic interpretation; unlike fractional diffusion which was based upon fractional integrals. Although the fractional initial-value problem was well-defined, and the solution was finite at all times, its values diverged as the time approached zero.

Fractional Diffusion Based on Riemann-Liouville Fractional Derivatives. R.Hilfer: Journal of Physical Chemistry B, 2000, 104[16], 3914-7