The authors derive a one-phase one-dimensional Stefan model with a time-fractional Riemann-Liouville flux and obtain a PDE with a singular source term plus the boundary condition Tx(s(t),t)=0.
A New Mathematical Formulation for a Phase Change Problem with a Memory Flux
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abstract
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.
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A note about fractional Stefan problem
The authors derive a one-phase one-dimensional Stefan model with a time-fractional Riemann-Liouville flux and obtain a PDE with a singular source term plus the boundary condition Tx(s(t),t)=0.