Explicit solutions to fractional Stefan-like problems for Caputo and Riemann–Liouville derivatives

Abstract

Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order α ∈ (0, 1) verifying that they coincide with the same classical Stefan problem at the limit case when α=1. For both problems, explicit solutions in terms of the Wright functions are presented. Even though the similarity of the two solutions, a proof that they are different is also given. The convergence when α↗1 of the one and the other solutions to the same classical solution is also given. Numerical examples for the dimensionless version of the problem are presented and analyzed.