Geodesic
Nonlocal boundary value problem for a~Lykov's type system of~first-order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 140-150.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove the unique solution of the problem with a shift to a Lykov's type system of differential equations of first order. The proof is given for different values of the generalized operators of fractional integro-differentiation included in the boundary condition.
Keywords: nonlocal value boundary problem, system of differential equations, integral equations. 
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O. A. Repin; S. K. Kumykova. Nonlocal boundary value problem for a~Lykov's type system of~first-order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 140-150. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a18/

[1] Lykov A. V., “Application of methods of thermodynamics of irreversible process to heat and mass transfer problems”, Inzh.-fiz. Zh., 9:3 (1965), 287–304

[2] Bitsadze A. V., Some classes of partial differential equations, Nauka, Moscow, 1981, 448 pp. | MR | Zbl

[3] Gellerstedt S., “Sur une équation linéaire aux dérivées partielles de type mixte”, Ark. Mat. Astron. Fys. A, 25:29 (1937), 1–23 | Zbl

[4] Nakhushev A. M., “On the Darboux problem for hyperbolic equations”, Sov. Math., Dokl., 195:4 (1970), 1567–1570 | MR | Zbl

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

[6] 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

[7] Smirnov M. M., Degenerate hyperbolic equations, Vyssh. shk., Minsk, 1977, 160 pp. | MR | Zbl

[8] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher transcendental functions, v. I, ed. H. Bateman, McGraw-Hill Book Co, Inc., New York – Toronto – London, 1953, 302 pp. | MR | Zbl

[9] Repin O. A., “Solvability of a problem with boundary conditions on characteristics for a degenerate hyperbolic equation”, Differ. Equations, 34:1 (1998), 113–116 | MR | Zbl

[10] Mihlin S. G., Lectures on linear integral equations, Fizmatlit, Moscow, 1959, 232 pp. | MR

[11] Srivastava N. M., Saigo M., “Multiplication of fractional calculus operators and boundary value problems involving the Euler–Darboux equation”, J. Math. Anal. Appl., 121:2 (1987), 325–369 | DOI | MR | Zbl

[12] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integrals and series. Elementary functions, Nauka, Moskva, 1981, 799 pp. | MR | Zbl