On a problem with generalized operators of fractional differentiation for a degenerated inside a domain hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 52-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider a problem with Saigo operators of fractional differentiation in a boundary condition on a characteristic part of a boundary. The unique solvability of this problem is proved.
Keywords: integral and derivative of Riemann–Liouville fractional order, integral equations of Fredholm, Gauss hypergeometric function, kernel resolvent.
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O. A. Repin; S. K. Kumykova. On a problem with generalized operators of fractional differentiation for a degenerated inside a domain hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2012), pp. 52-60. http://geodesic.mathdoc.fr/item/VSGU_2012_9_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, 161 pp. | MR | Zbl

[3] Repin O. A., Kraevye zadachi so smescheniem dlya uravnenii giperbolicheskogo i smeshannogo tipov, Izd-vo Saratov. gos. un-ta, Saratov, 1992, 688 pp. | MR

[4] Kumykova S. K., “Kraevaya zadacha so smescheniem dlya vyrozhdayuschegosya vnutri oblasti giperbolicheskogo uravneniya”, Differents. uravneniya, 16:1 (1980), 93–104 | MR | Zbl

[5] Nakhushev A. M., “Novaya kraevaya zadacha dlya odnogo vyrozhdayuschegosya giperbolicheskogo uravneniya”, DAN SSSR, 187:4 (1969), 736–739 | Zbl

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

[7] Trikomi F., Lektsii po uravneniyam v chastnykh proizvodnykh, Inostr. lit., M., 1957, 443 pp.

[8] Kumykova S. K., Nakhusheva F. B., “Ob odnoi kraevoi zadache dlya giperbolicheskogo uravneniya, vyrozhdayuschegosya vnutri oblasti”, Differents. uravneniya, 14:1 (1978), 50–65 | MR | Zbl

[9] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 1, Gipergeometricheskaya funktsiya. Funktsiya Lezhandra, Nauka, M., 1973, 296 pp.

[10] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968, 511 pp. | MR