  A mathematical model for a one-phase change problem (particularly a Stefan
problem) with a memory flux, is obtained. The hypothesis that the weighted sum
of fluxes back in time is proportional to the gradient of temperature is
considered. The model obtained involves fractional derivatives with respect on
time in the sense of Caputo and in the sense of Riemann--Liouville. An integral
relationship for the free boundary which is equivalent to the `fractional
Stefan condition' is also obtained.
