Two different fractional Stefan problems that are convergent to the same classical Stefan problem

摘要

Two fractional Stefan problems are considered by using Riemann-Liouville andCaputo derivatives of order $lpha in (0,1)$ such that in the limit case($lpha =1$) both problems coincide with the same classical Stefan problem.For the one and the other problem, explicit solutions in terms of the Wrightfunctions are presented. We prove that these solutions are different eventhough they converge, when $lpha earrow 1$, to the same classical solution.This result also shows that some limits are not commutative when fractionalderivatives are used.