Geodesic
Problem with shift for the third-order equation with discontinuous coefficients
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 17-25.

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The unique solvability of boundary value problem with Saigo operators for the third-order equation with multiple characteristics was investigated. The uniqueness theorem with constraints of inequality type on the known functions and different orders of generalized fractional integro-differentiation was proved. The existence of solution is equivalently reduced to the solvability of Fredholm integral equation of the second kind.
Keywords: boundary value problem, Gauss hypergeometric function, operators of fractional order, Fredholm equation. 
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O. A. Repin; S. K. Kumykova. Problem with shift for the third-order equation with discontinuous coefficients. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 17-25. http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a1/

[1] Saigo M., “A remark on integral operators involving the Gauss hypergeometric functions”, Math. Rep. Kyushu Univ., 11:2 (1977/78), 135–143 | MR | Zbl

[2] Samko S. G., Kilbas A. A., Marichev O. I., Integrals and derivatives of fractional order and some of their applications, Nauka i Tekhnika, Minsk, 1987, 688 pp. | MR | Zbl

[3] Repin O. A., Boundary value problems with shift for equations of hyperbolic and mixed type, Izd-vo Saratovskogo Universiteta, Samarskiy Filial, Samara, 1992, 164 pp. | MR | Zbl

[4] Eleev V. A., Kumykova S. K., “The inner boundary value problem for mixed-type equation of third order with multiple characteristics”, Izvestiya Kabardino-Balkarskogo nauchnogo tsentra RAN, 2010, no. 5(37), Part 2, 5–14

[5] Repin O. A., Kumykova S. K., “Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2011, no. 4(25), 25–36 | DOI

[6] Repin O. A., Kumykova S. K., “On a boundary value problem with shift for an equation of mixed type in an unbounded domain”, Diff. Equ., 48:8, 1127–1136 | DOI | MR | MR | Zbl

[7] Smirnov M. M., Equations of mixed type, Nauka, Moscow, 1970, 295 pp. | MR

[8] Tricomi F., Lectures on partial differential equations, Inostr. Lit., Moscow, 1957, 443 pp.

[9] Dzhuraev T. D., Boundary value problems for equations of mixed and mixed-composite types, Fan, Tashkent, 1979, 239 pp. | MR | Zbl

[10] Handbook of mathematical functions with formulas, graphs and mathematical tables, eds. M. Abramowitz, I. Stegun, Nauka, Moscow, 1979, 831 pp. | MR