  A fractional diffusion equation based on Riemann-Liouville fractional
derivatives is solved exactly. The initial values are given as fractional
integrals. The solution is obtained in terms of $H$-functions. It differs from
the known solution of fractional diffusion equations based on fractional
integrals. The solution of fractional diffusion based on a Riemann-Liouville
fractional time derivative does not admit a probabilistic interpretation in
contrast with fractional diffusion based on fractional integrals. While the
fractional initial value problem is well defined and the solution finite at all
times its values for $t\to 0$ are divergent.
