Geodesic
Modeling of freezing processes by an one-dimensional thermal conductivity equation with fractional differentiation operators
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 376-387

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We have studied the Stefan problem with Caputo fractional order time derivatives. The difference scheme is built. The algorithm and the program for a numerical solution of the Stefan problem with fractional differentiation operator are created. For the given entry conditions and freezing ground parameters we have obtained the space-time temperature dependences for different values of parameter $\alpha $. The functional dependences of the interface motion for the generalized Stefan conditions depending on the value of $\alpha $ are estimated. Finally we have found that the freezing process is slowed down during the transition to fractional derivatives.
Keywords: Caputo fractional derivative, Stefan problem, the memory effect, difference scheme, heat conductivity, phase boundary.
Mots-clés : fractal structure, phase transition 
@article{VSGTU_2017_21_2_a10,
     author = {V. D. Beybalaev and A. A. Aliverdiev and R. A. Magomedov and R. R. Meilanov and E. N. Akhmedov},
     title = {Modeling of freezing processes by an one-dimensional thermal conductivity equation with fractional differentiation operators},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {376--387},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a10/}
}
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V. D. Beybalaev; A. A. Aliverdiev; R. A. Magomedov; R. R. Meilanov; E. N. Akhmedov. Modeling of freezing processes by an one-dimensional thermal conductivity equation with fractional differentiation operators. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 376-387. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a10/