[1]
|
Alexiades, V. and Solomon, A.D. (1993) Mathematical Modelling of Melting and Freezing Processes. Hemisphere-Taylor & Francis, Washington DC.
|
[2]
|
Cannon, J.R. (1984) The One-Dimensional Heat Equation. Addison-Wesley, Menlo Park.
http://dx.doi.org/10.1017/CBO9781139086967
|
[3]
|
Carslaw, H.S. and Jaeger, J.C. (1959) Conduction of Heat in Solids. Clarendon Press, Oxford.
|
[4]
|
Crank, J. (1984) Free and Moving Boundary Problem. Clarendon Press, Oxford.
|
[5]
|
Fasano, A. (2005) Mathematical Models of Some Diffusive Processes with Free Boundary. MAT-Series A, 11, 1-128.
|
[6]
|
Gupta, S.C. (2003) The Classical Stefan Problem. Basic Concepts, Modelling and Analysis. Elsevier, Amsterdam.
|
[7]
|
Lunardini, V.J. (1991) Heat Transfer with Freezing and Thawing. Elsevier, London.
|
[8]
|
Rubinstein, L.I. (1971) The Stefan Problem. American Mathematical Society, Providence.
|
[9]
|
Tarzia, D.A. (2000) A Bibliography on Moving-Free Boundary Problems for the Heat-Diffusion Equation. The Stefan and Related Problems. MAT-Series A, 2, 1-297.
|
[10]
|
Tarzia, D.A. (2011) Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface. In: El-Amin, M., Ed., Advanced Topics in Mass Transfer, InTech Open Access Publisher, Rijeka, 439-484.
|
[11]
|
Tarzia, D.A. (1981) An Inequality for the Coefficient of the Free Boundary of the Neumann Solution for the Two-Phase Stefan Problem. Quarterly of Applied Mathematics, 39, 491-497.
|
[12]
|
Tarzia, D.A. (1982) Determination of the Unknown Coefficients in the Lamé-Clapeyron-Stefan Problem (Or One-Phase Stefan Problem. Advances in Applied Mathematics, 3, 74-82. http://dx.doi.org/10.1016/S0196-8858(82)80006-7
|
[13]
|
Kilbas, A., Srivastava, H. and Trujillo, H. (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam.
|
[14]
|
Mainardi, F. (2010) Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press, London.
|
[15]
|
Podlubny, S.I. (1999) Fractional Differential Equations. Academic Press, San Diego.
|
[16]
|
Gorenflo, R., Luchko, Y. and Mainardi, F. (1999) Analytical Properties and Applications of the Wright Function. Fractional Calculus and Applied Analysis, 2, 383-414.
|
[17]
|
Luchko, Y. (2010) Some Uniqueness and Existence Results for the Initial-Boundary-Value Problems for the Generalized Time-Fractional Diffusion Equation. Computers & Mathematics with Applications, 59, 1766-1772.
http://dx.doi.org/10.1016/j.camwa.2009.08.015
|
[18]
|
Mainardi, F., Luchko, Y. and Pagnini, G. (2001) The Fundamental Solution of the Space-Time Fractional Diffusion Equation. Fractional Calculus and Applied Analysis, 4, 153-192.
|
[19]
|
Mainardi, F., Mura, F. and Pagnini, G. (2010) The M-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey. International Journal of Differential Equations, 2010, Article ID: 104505.
|
[20]
|
Falcini, F., Garra, V. and Voller, V.R. (2013) Fractional Stefan Problems Exhibiting Lumped and Distributed Latent-Heat Memory Effects. Physical Review E, 87, Article ID: 042401.
|
[21]
|
Jinyi, L. and Mingyu, X. (2009) Some Exact Solutions to Stefan Problems with Fractional Differential Equations. Journal of Mathematical Analysis and Applications, 351, 536-542. http://dx.doi.org/10.1016/j.jmaa.2008.10.042
|
[22]
|
Kholpanov, L.P., Zaklev, Z.E. and Fedotov, V.A. (2003) Neumann-Lamé-Clapeyron-Stefan Problem and Its Solution Using Fractional Differential-Integral Calculus. Theoretical Foundations of Chemical Engineering, 37, 113-121.
|
[23]
|
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
|
[24]
|
Roscani, S. and Tarzia, D.A. (2014) A Generalized Neumann Solution for the Two-Phase Fractional Lamé-Clapeyron-Stefan Problem. Advances in Mathematical Sciences and Applications, 24, 237-249.
|
[25]
|
Voller, V.R. (2010) An Exact Solution of a Limit Case Stefan Problem Governed by a Fractional Diffusion Equation. International Journal of Heat and Mass Transfer, 53, 5622-5625.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.07.038
|
[26]
|
Voller, V.R. (2014) Fractional Stefan Problems. International Journal of Heat and Mass Transfer, 74, 269-277.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.008
|
[27]
|
Caputo, M. (1967) A Model of Dissipation Whose Q Is Almost Frequency Independent—II. Geophysical Journal International, 13, 529-539. http://dx.doi.org/10.1111/j.1365-246X.1967.tb02303.x
|
[28]
|
Wright, E.M. (1933) On the Coefficients of Power Series Having Exponential Singularities. Journal of the London Mathematical Society, 8, 71-79. http://dx.doi.org/10.1112/jlms/s1-8.1.71
|