Numerical-analytical method for solving the modified Сauchy problem for the fractional diffusion equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 175-183 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper considers a numerical-analytical method for efficient search for an approximate solution of the modified Cauchy problem for a parabolic differential equation with a fractional time derivative in the sense of Riemann-Liouville, which naturally arises in the study of nonlinear features of moisture-salt transfer processes in media with a fractal structure of pore space
Mots-clés : diffusion equation, fractal structure
Keywords: fractional differentiation operator, numerical-analytical method, discrete analog, moisture transfer, algorithm.
@article{VKAM_2022_39_2_a11,
     author = {L. I. Serbina},
     title = {Numerical-analytical method for solving the modified {{\CYRS}auchy} problem for the fractional diffusion equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {175--183},
     year = {2022},
     volume = {39},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a11/}
}
TY  - JOUR
AU  - L. I. Serbina
TI  - Numerical-analytical method for solving the modified Сauchy problem for the fractional diffusion equation
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2022
SP  - 175
EP  - 183
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a11/
LA  - ru
ID  - VKAM_2022_39_2_a11
ER  - 
%0 Journal Article
%A L. I. Serbina
%T Numerical-analytical method for solving the modified Сauchy problem for the fractional diffusion equation
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2022
%P 175-183
%V 39
%N 2
%U http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a11/
%G ru
%F VKAM_2022_39_2_a11
L. I. Serbina. Numerical-analytical method for solving the modified Сauchy problem for the fractional diffusion equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 175-183. http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a11/

[1] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981, 448 pp.

[2] Nerpin S. V., Chudnovskii A. F., Energo i massoobmen v sisteme rastenie-pochva-vozdukh, Gidrometizdat, L., 1975, 358 pp.

[3] Chudnovskii A. F., Teplofizika pochv, Nauka, M., 1976, 352 pp.

[4] Sobolev S. L., “Lokalno-neravnovesnye modeli protsessov perenosa”, Uspekhi fiz. nauk, 167:10 (1997), 1096-1106

[5] Kochubei A. N., “Diffuziya drobnogo poryadka”, Diff. uravn., 26:4 (1990), 660-670

[6] Fedotov G. N., Tretyakov Yu. D., Ivanov V. K., Kuklin A. I., Pakhomov E. I., Islamov A. Kh., Pochatkova T. N., “Vliyanie vlazhnosti na fraktalnye svoistva pochvennykh kolloidov”, DAN, 409:2 (2006), 199-201

[7] Serbina L. I., Nelokalnye matematicheskie modeli protsessov perenosa v sistemakh s fraktalnoi strukturoi, Izd-vo KBNTs RAN, Nalchik, 2002, 144 pp.

[8] Nigmatullin R.R., “Drobnyi integral i ego fizicheskaya interpretatsiya”, Teor. i mat. fizika, 1992, no. 3, 354-368

[9] Nakhushev A. M., Elementy drobnogo ischisleniya i ikh primenenie, Fizmatlit, M., 2003, 272 pp.

[10] Serbina L. I., “Ob odnoi matematicheskoi modeli perenosa substantsii vo fraktalnykh sredakh”, Mat. modelirovanie, 15:9 (2005), 17–28

[11] Nakhushev A. M., “Nagruzhnye uravneniya i ikh prilozheniya”, Diff. uravn., 19:1 (1983), 86-94

[12] Lavrentev M. M., Savelev L. Ya., Teoriya operatorov i nekorrektnye zadachi, Novosibirsk, 1999

[13] Golovizin V. M., Kisilev V. P., Korotkin I. A., Yurkov Yu. I., Nekotorye osobennosti vychislitelnykh algoritmov dlya uravnenii drobnoi diffuzii, Preprint IBRAE RAN, M., 2002, 57 pp.

[14] Samarskii A. A., Vvedenie v chislennye metody, Nauka, M., 1997, 240 pp.

[15] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Minsk, 1987, 688 pp.