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Статья
2015

A nonlocal problem with generalized fractional differential operators for a mixed-type equation in an unbounded domain


O. A. RepinO. A. Repin, S. K. KumykovaS. K. Kumykova
Русская математика
https://doi.org/10.3103/S1066369X15040076
Abstract / Full Text

For a mixed-type equation we study a problem with generalized fractional differential operators whose kernels contain Gauss hypergeometric functions. We prove the unique solvability of the stated boundary value problem under constraints in the form of inequalities imposed on the known functions with various parameters of operators.

Author information
  • Samara State Economic University, 141 ul. Sovetskoi Armii 141, Samara, 443090, RussiaO. A. Repin
  • Kabardino-Balkarian State University, ul. Chernyshevskogo 173, Nal’chik, 360004, RussiaS. K. Kumykova
References
  1. Saigo, M. “A Remark on Integral Operators Involving the Gauss Hypergeometric Function,” Math. Rep. Kyushu Univ. 11(2), 135–143 (1978).
  2. Samko, R. G., Kilbas, A. A., and Marichev, O. I. Fractional Integrals and Derivatives and Their Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].
  3. Repin, O. A. Boundary Value Problems with Shift for Equations of Hyperbolic and Mixed Types (Saratovsk. Gos. Univ., Samarsk. Fil., 1992) [in Russian].
  4. Repin, O. A., Kumykova, S. K. “A Nonlocal Problem with Fractional Derivatives for the Mixed Type Equation,” Russian Mathematics (Iz. VUZ) 58, No. 8, 65–70 (2014).
  5. Smirnov, M. M. Degenerate Elliptic and Hyperbolic Equations (Nauka, Moscow, 1966) [in Russian].
  6. Kumykova, S. K. “A Problem with Nonlocal Conditions on Characteristics for a Mixed-Type Equation,” Differ. Uravn. 10(1), 78–88 (1974).
  7. Repin, O. A., Kumykova, S. K. “On a Boundary Value Problem with Shift for an Equation of Mixed Type in an Unbounded Domain,” Differ. Equ. 48, No. 8, 1127–1136 (2012).
  8. Muskhelishvili, N. I. Singular Integral Equations (Nauka, Moscow, 1968) [in Russian].