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

2020/01/29 by Sabrina Roscani, N. Caruso, Nahuel Caruso +2
Mathematics · #Applied mathematics #Calculus (dental) #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Fractional calculus #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Differential Equations Analysis #Riemann hypothesis #math.AP #msc:26A33 #msc:35C05 #msc:35R35

paper · pdf · doi:10.1016/j.cnsns.2020.105361

21 pages

arxiv created 2020/01/29 · openalex publication_date 2020/05/27 · arxiv updated 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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\nearrow 1 of the one and the other solutions to the same classical solution is given. Numerical examples for the dimensionless version of the problem are also presented and analyzed.

Citations