Abstract
In the characteristic triangle for a hyperbolic equation of the second kind we study a nonlocal problem, where the boundary value condition contains a linear combination of Riemann–Liouville fractional integro-differentiation operators. We establish variation intervals of orders of fractional integro-differentiation operators, taking into account parameters of the considered equation with which the mentioned problem has either a unique solution or more than one solution.
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References
Nakhushev, A.M. Fractional Calculus and its Applications (Fizmatlit, Moscow, 2003) [in Russian].
Samko, S. G., Kilbas, A. A., and Marichev, O. I. Fractional Integrals and Derivatives. Theory and Applications (Nauka i Tekhnika,Minsk, 1987) [in Russian].
Nakhushev, A. M. Problems with Shift for Partial Differential Equations (Nauka, Moscow, 2006) [in Russian].
Smirnov, M. M. Degenerate Hyperbolic Eequations (Vyssh. Shkola,Minsk, 1977) [in Russian].
Smirnov, M. M. Mixed Type Equations (Vyssh. Shkola,Moscow, 1985) [in Russian].
Orazov, I. “A Boundary-Value Problem with Displacement for a Generalized Tricomi Equation”, Differ. Equations 17, No. 2, 235–246 (1981).
Repin, O. A. and Kumykova, S. K. “A Nonlocal Problem for the Bitsadze–Lykov Equation”, Russian Mathematics (Iz. VUZ) 54, No. 3, 24–30 (2010).
Repin,O. A. and Kumykova, S.K. “A Problem with Generalized Fractional Integro-DifferentiationOperators of Arbitrary Order”, RussianMathematics (Iz. VUZ) 56, No. 12, 50–60 (2012).
Lebedev, N. N. Special Functions and Their Applications (Fizmatgiz, Moscow, 1963) [in Russian].
Tricomi, F. Integral Equations (Interscience Publishers, Inc., New York, 1957; In. Lit.,Moscow, 1960).
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Original Russian Text © O.A. Repin, S.K. Kumykova, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 9, pp. 51–58.
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Repin, O.A., Kumykova, S.K. On the solvability of a nonlocal problem for a hyperbolic equation of the second kind. Russ Math. 60, 46–52 (2016). https://doi.org/10.3103/S1066369X1609005X
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DOI: https://doi.org/10.3103/S1066369X1609005X