Roscani, S. and Marcus, E. (2013) Two Equivalent Stefan’s Problems for the Time-Fractional Diffusion Equation. Fractional Calculus and Applied Analysis, 16, 802-815.
http://dx.doi.org/10.2478/s13540-013-0050-7

has been cited by the following article:

• TITLE: Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lamé-Clapeyron-Stefan Problem

  AUTHORS: Domingo Alberto Tarzia

  KEYWORDS: Free Boundary Problems, Fractional Diffusion, Lamé-Clapeyron-Stefan Problem, Unknown Thermal Coefficients, Explicit Solution, Over-Specified Boundary Condition

  JOURNAL NAME: Applied Mathematics, Vol.6 No.13, November 30, 2015

  ABSTRACT: We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lamé-Clapeyron-Stefan problem with an over-specified boundary condition on the fixed face . The partial differential equation and one of the conditions on the free boundary include a time Caputo’s fractional derivative of order . Moreover, we obtain the necessary and sufficient conditions on data in order to have a unique solution by using recent results obtained for the fractional diffusion equation exploiting the properties of the Wright and Mainardi functions, given in: 1) Roscani-Santillan Marcus, Fract. Calc. Appl. Anal., 16 (2013), 802 - 815; 2) Roscani-Tarzia, Adv. Math. Sci. Appl., 24 (2014), 237 - 249 and 3) Voller, Int. J. Heat Mass Transfer, 74 (2014), 269 - 277. This work generalizes the method developed for the determination of unknown thermal coefficients for the classical Lamé-Clapeyron-Stefan problem given in Tarzia, Adv. Appl. Math., 3 (1982), 74 - 82, which is recovered by taking the limit when the order .