2018/05/31 by Sabrina Roscani, Julieta Bollati, Domingo A. Tarzia +1
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Boundary (topology) #Flux (metallurgy) #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Phase (matter) #Phase change #Physics #Sense (electronics) #Stefan problem #Thermodynamics #Thermoelastic and Magnetoelastic Phenomena #math-ph #math.AP #math.MP #msc:26A33 #msc:33E20 #msc:35C05 #msc:35R35 #msc:80A22
paper · pdf · doi:10.1016/j.chaos.2018.09.023
published as Chaos, Solitons and Fractals, Vol. 116 (2018), p.p. 340-347 · 26 pages, 2 figures
openalex publication_date 2018/10/03 · arxiv created 2018/10/16 · arxiv updated 2018/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.