Geodesic
On a boundary-value problem with Saigo operators for a~mixed-type equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 271-277.

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The theory of mixed type equations is one of the most important parts of the theory of partial differential equations. This is due to the fact that equations of mixed type are connected with the problems of the theory of singular integral equations, integral transformations, and special functions. An actual continuation of the research in these fields will be the proof of the unique solvability of the inner-boundary problem. In the hyperbolic part of the domain, a condition is established that relates the generalized derivatives and fractional-order integrals to the Gauss hypergeometric function.
Keywords: boundary value problem, Gauss hypergeometric function, fractional-order operator, Cauchy problem, integral equations. 
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O. A. Repin. On a boundary-value problem with Saigo operators for a~mixed-type equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 271-277. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a4/

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

[2] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poriadka i nekotorye ikh prilozheniia [Integrals and derivatives of fractional order and some of their applications], Nauka i tekhnika, Minsk, 1987, 688 pp. (In Russian) | MR | Zbl

[3] Repin O. A., Kraevye zadachi so smeshcheniem dlia uravnenii giperbolicheskogo i smeshannogo tipov [Boundary value problems with shift for equations of hyperbolic and mixed type], Saratov University, Saratov, 1992, 161 pp. (In Russian) | MR | Zbl

[4] Repin O. A., Kumykova S. K., “Interior-boundary value problem with Saigo operators for the gellerstedt equation”, Differ. Equ., 49:10 (2013), 1307–1316 | DOI | MR | Zbl

[5] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh [Some classes of partial differential equations], Nauka, Moscow, 1981, 448 pp. (In Russian) | MR

[6] Bitsadze A. V., Boundary value problems for second order elliptic equations, North-Holland Series in Applied Mathematics and Mechanics, 5, North-Holland Publishing Company, Amsterdam, 1968, 211 pp. | MR | MR | Zbl

[7] Smirnov M. M., Uravneniia smeshannogo tipa [Equations of mixed type], Nauka, Moscow, 1970, 296 pp. (In Russian) | MR