Geodesic
On the solvability of nonlocal problem for a~hyperbolic equation of the second kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 51-58.

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In the characteristic triangle, for a hyperbolic equation of the second kind we study a nonlocal problem when boundary condition contains a linear combination of operators of fractional Riemann–Liouville integro-differentition. We establish intervals of change of orders of operators of fractional integro-differentiation associated with the parameters of the equation for which the problem is either uniquely solvable or has more than one solution.
Keywords: operators of fractional integro-differentiation, Volterra integral equation of the second kind, method of successive approximations. 
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O. A. Repin; S. K. Kumykova. On the solvability of nonlocal problem for a~hyperbolic equation of the second kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 51-58. http://geodesic.mathdoc.fr/item/IVM_2016_9_a4/

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

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

[3] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006

[4] Smirnov M. M., Vyrozhdayuschiesya giperbolicheskie uravneniya, Izd-vo Vyssh. shk., Minsk, 1977 | MR

[5] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shk., M., 1985 | MR

[6] Orazov I., “Ob odnoi kraevoi zadache so smescheniem dlya obobschennogo uravneniya Trikomi”, Differents. uravneniya, 17:2 (1981), 339–344 | MR

[7] Repin O. A., Kumykova S. K., “Nelokalnaya zadacha dlya uravneniya Bitsadze–Lykova”, Izv. vuzov. Matem., 2010, no. 3, 28–35 | MR | Zbl

[8] Repin O. A., Kumykova S. K., “Zadacha s obobschennymi operatorami drobnogo integro-differentsirovaniya proizvolnogo poryadka”, Izv. vuzov. Matem., 2012, no. 12, 59–71 | MR | Zbl

[9] Lebedev N. N., Spetsialnye funktsii i ikh prilozheniya, Fizmatgiz, M., 1963 | MR

[10] Trikomi F., Integralnye uravneniya, In. lit., M., 1960 | MR