Geodesic
A boundary-value problem with shifted for a~mixed type equation with fractional derivative
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 89-94.

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A non-local problem for a mixed type equation with partial fractional derivative of Riemann–Liouville is studied, boundary condition of which contains linear combination of generalized operators of fractional integro-differentiation. Unique solvability of the problem is then proved. 
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O. A. Repin; S. A. Sayganova. A boundary-value problem with shifted for a~mixed type equation with fractional derivative. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 89-94. http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a11/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp. | MR | Zbl

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

[3] Kilbas A. A., Repin O. A., “Nelokalnaya zadacha dlya uravneniya smeshannogo tipa s chastnoi proizvodnoi Rimana–Liuvillya i operatorami obobschennogo drobnogo integrirovaniya v kraevom uslovii”, Trudy In-ta matematiki (Minsk), 12:2 (2004), 75–81

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

[5] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp. | Zbl

[6] Pskhu A. V., Reshenie kraevykh zadach dlya differentsialnykh uravnenii s chastnymi proizvodnymi drobnogo poryadka, Soobsch. Nauchn.-issled. in-ta priklad. matematiki i avtomatizatsii KBNTs RAN, Izd-vo NII PMA KBNTs RAN, Nalchik, 2001, 43 pp.

[7] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 3, Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967, 299 pp. | MR

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

[9] Trikomi F., Lektsii po uravneniyam v chastnykh proizvodnykh, Iz-vo inostr. lit., M., 1957, 443 pp.

[10] Saigo M., Kilbas A. A., “Generalized fractional integrals and derivatives in Hölder space”, Transforms Methods Special Functions, Proc. Intern. Workshop (Sofia, 12–12 August 1994), Singapore, 1995, 282–293 | Zbl

[11] Kilbas A. A., Integralnye uravneniya: kurs lektsii, BGU, Minsk, 2005, 143 pp. | Zbl