  In a fractional Cauchy problem, the usual first order time derivative is
replaced by a fractional derivative. The fractional derivative models time
delays in a diffusion process. The order of the fractional derivative can be
distributed over the unit interval, to model a mixture of delay sources. In
this paper, we provide explicit strong solutions and stochastic analogues for
distributed-order fractional Cauchy problems on bounded domains with Dirichlet
boundary conditions. Stochastic solutions are constructed using a non-Markovian
time change of a killed Markov process generated by a uniformly elliptic second
order space derivative operator.
