  The time-fractional diffusion equation is considered, where the time
derivative is either of Caputo or Riemann-Liouville type. The solution of a
general initial-boundary value problem with time-dependent boundary conditions
over bounded and unbounded domains is derived using the embedding method. The
solution of the initial-boundary value problem, expressed in terms of a
two-parameter auxiliary function, is used to obtain analytical solutions of
moving boundary problems. In particular, a 'fractional' analogue of the Neumann
solution to a classical Stefan problem for melting ice is found.
