Geodesic
Boundary-Value Problems for a Wave Equation of Fractional Order
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 44-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

A nonlocal wave equation with variable coefficients in a rectangular domain is considered. The first and third boundary-value problems in the differential form are examined; the method of lines in the difference form is applied for solving these problems. For the system of difference equations with constant coefficients arising from the method of lines, a solution is obtained.
Keywords: nonlocal wave equation, fractional derivative, method of lines, a priori estimate. 
@article{INTO_2018_149_a5,
     author = {M. A. Kerefov and B. M. Kerefov},
     title = {Boundary-Value {Problems} for a {Wave} {Equation} of {Fractional} {Order}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {44--55},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/}
}
TY  - JOUR
AU  - M. A. Kerefov
AU  - B. M. Kerefov
TI  - Boundary-Value Problems for a Wave Equation of Fractional Order
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2018
SP  - 44
EP  - 55
VL  - 149
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/
LA  - ru
ID  - INTO_2018_149_a5
ER  - 
%0 Journal Article
%A M. A. Kerefov
%A B. M. Kerefov
%T Boundary-Value Problems for a Wave Equation of Fractional Order
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2018
%P 44-55
%V 149
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/
%G ru
%F INTO_2018_149_a5
M. A. Kerefov; B. M. Kerefov. Boundary-Value Problems for a Wave Equation of Fractional Order. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 44-55. http://geodesic.mathdoc.fr/item/INTO_2018_149_a5/

[1] Alikhanov A. A., “Apriornye otsenki reshenii kraevykh zadach dlya uravnenii drobnogo poryadka”, Differ. uravn., 46:5 (2010), 658–664 | MR | Zbl

[2] Berezin I. S., Zhidkov N. P., Metody vychislenii, GIFML, 1962

[3] Gekkieva S. Kh., “Kraevaya zadacha dlya obobschennogo uravneniya perenosa s drobnoi proizvodnoi po vremeni”, Dokl. Adyg. Mezhdunar. AN, 1:1 (1994), 16–19

[4] Kerefov M. A., “Pervaya kraevaya zadacha dlya nelokalnogo volnovogo uravneniya”, Nauch. vedomosti BelGU. Ser. mat. Fiz., 42:6 (227) (2016), 20–23

[5] Kumykova S. K., “Ob odnoi kraevoi zadache dlya uravneniya $\operatorname{sign}|y|^mu_{xx}+u_{yy}=0$”, Differ. uravn., 12:1 (1976), 79–88 | MR | Zbl

[6] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973

[7] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003

[8] Olemskoi A. I., Flat A. Ya., “Ispolzovanie kontseptsii fraktala v fizike kondensirovannoi sredy”, Usp. fiz. nauk, 163:12 (1993), 1–50 | DOI

[9] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005