Geodesic
Nonlocal problem with Saigo operators for mixed type equation of the third order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 63-68.

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

For a third order equation with multiple characteristics we investigate a boundary-value problem with Saigo operators. We prove the unique solvability of the problem for various values of the parameters of generalized fractional integro-differentiation operators.
Keywords: boundary-value problem, the hypergeometric function of Gauss, Saigo operator, Fredholm integral equation. 
@article{IVM_2019_1_a5,
     author = {O. A. Repin},
     title = {Nonlocal problem with {Saigo} operators for mixed type equation of the third order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--68},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_1_a5/}
}
TY  - JOUR
AU  - O. A. Repin
TI  - Nonlocal problem with Saigo operators for mixed type equation of the third order
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 63
EP  - 68
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_1_a5/
LA  - ru
ID  - IVM_2019_1_a5
ER  - 
%0 Journal Article
%A O. A. Repin
%T Nonlocal problem with Saigo operators for mixed type equation of the third order
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 63-68
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_1_a5/
%G ru
%F IVM_2019_1_a5
O. A. Repin. Nonlocal problem with Saigo operators for mixed type equation of the third order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2019), pp. 63-68. http://geodesic.mathdoc.fr/item/IVM_2019_1_a5/

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

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

[3] Repin O. A., Kraevye zadachi so smescheniem dlya uravnenii giperbolicheskogo i smeshannogo tipov, Saratovsk. un-t, 1992

[4] Repin O. A., Kumykova S. K., “Zadacha so smescheniem dlya uravneniya tretego poryadka s razryvnymi koeffitsientami”, Vestn. Samarsk. gos. tekhn. un-ta. Ser. fiz.-matem. nauki, 2012, no. 4(29), 17–25 | DOI

[5] Smirnov M. M., Uravneniya smeshannogo tipa, Nauka, M., 1970

[6] Kilbas A. A., Repin O. A., “Analog zadachi Bitsadze–Samarskogo dlya uravneniya smeshannogo tipa s drobnoi proizvodnoi,”, Differents. uravneniya, 39:5 (2003), 638–644 | Zbl

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

[8] Saigo M., Kilbas A. A., “Generalized fractional integrals and derivatives in Hölder spaces”, Transform methods and special functions, Proc. 1-st internat. workshop (Bankya, Bulgaria, August 12–17, 1994), eds. Rusev P. et al., SCT Publishing, Sofia, 1995, 282–293 | MR | Zbl

[9] Kilbas A. A., Integralnye uravneniya: kurs lektsii, Izd-vo BGU, Minsk, 2005