Geodesic
On solvability of nonlocal problem for loaded parabolic-hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 62-69.

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

We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.
Mots-clés : boundary-value problem, equation of mixed type, operators of fractional integro-differentiation in the Riemann–Liouville sense, generalized operators of fractional integro-differentiation in the M. Saigo sense, Fredholm integral equation of the second kind. 
@article{IVM_2018_3_a6,
     author = {A. V. Tarasenko},
     title = {On solvability of nonlocal problem for loaded parabolic-hyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--69},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/IVM_2018_3_a6/}
}
TY  - JOUR
AU  - A. V. Tarasenko
TI  - On solvability of nonlocal problem for loaded parabolic-hyperbolic equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 62
EP  - 69
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/IVM_2018_3_a6/
LA  - ru
ID  - IVM_2018_3_a6
ER  - 
%0 Journal Article
%A A. V. Tarasenko
%T On solvability of nonlocal problem for loaded parabolic-hyperbolic equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 62-69
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/IVM_2018_3_a6/
%G ru
%F IVM_2018_3_a6
A. V. Tarasenko. On solvability of nonlocal problem for loaded parabolic-hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2018), pp. 62-69. https://geodesic-test.mathdoc.fr/item/IVM_2018_3_a6/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987

[2] Saigo M., “A remark on integral operators involving the Gauss hypergeometric function”, Math. Rep. Kyushu Univ., 11:2 (1978), 135–143 | MR | Zbl

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

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

[5] Kochubei A. N., “Diffuziya drobnogo poryadka”, Differents. uravneniya, 26:4 (1990), 660–670 | MR | Zbl

[6] Repin O. A., Tarasenko A. V., “Nelokalnaya zadacha dlya uravneniya s chastnoi proizvodnoi drobnogo poryadka”, Vestn. Samarsk. gos. tekhn. un-ta. Ser. fiz.-matem. nauki, 19:1 (2015), 78–86 | DOI

[7] Repin O. A., Kumykova S. K., “Ob odnom klasse nelokalnykh zadach dlya giperbolicheskogo uravneniya s vyrozhdeniem tipa i poryadka”, Vestn. Samarsk. gos. tekhn. un-ta. Ser. fiz.-matem. nauki, 2014, no. 4(37), 22–32

[8] Gekkieva S. Kh., “Analog zadachi Trikomi dlya uravneniya smeshannogo tipa s drobnoi proizvodnoi”, Izv. Kabardino-Balkarsk. nauchnogo tsentra RAN, 2001, no. 2(7), 78–80

[9] Trikomi F., Lektsii po uravneniyam v chastnykh proizvodnykh, In. lit., M., 1957

[10] Bugrov Ya. S., Nikolskii S. M., Vysshaya matematika, Uchebnik dlya vuzov, v. 3, Differentsialnye uravneniya. Kratnye integraly. Ryady. Funktsii kompleksnogo peremennogo, Drofa, M., 2004