Geodesic
Mathematical model of a~heat transfer in fractal structure medium
Matematičeskoe modelirovanie, Tome 21 (2009) no. 5, pp. 55-62

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There was considered mathematical model of a heat transfer. A theorem of existence and uniqueness of solution of boundary-value for the generalized Caputo on a half-line was proved. Implicit difference scheme of task solution of heat transfer with a derived fractional-order through the time and a space variable were constructed. Criterions of stability of these implicit difference schemes were proved. 
@article{MM_2009_21_5_a4,
     author = {V. D. Beybalaev},
     title = {Mathematical model of a~heat transfer in fractal structure medium},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {55--62},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_5_a4/}
}
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V. D. Beybalaev. Mathematical model of a~heat transfer in fractal structure medium. Matematičeskoe modelirovanie, Tome 21 (2009) no. 5, pp. 55-62. http://geodesic.mathdoc.fr/item/MM_2009_21_5_a4/