Nonlocal problem for degenerating hyperbolic equation

O. A. Repin^a, S. K. Kumykova<sup>b

a</sup> Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia
^b Kabardino-Balkarian State University, 173 Chernyshevskogo str., Nalchik, 360004 Russia

Abstract: We investigate a nonlocal problem for a degenerating hyperbolic equation in the domain, which is bounded by the characteristics of the equation. Boundary conditions include a linear combination of operators of fractional in the sense of Riemann-Liouville integrodifferentiation. The uniqueness of solution of the problem is proved by a modified Tricomi method. The existence is reduced to the equivalent of the solvability of a singular integral equation with Cauchy kernel or Fredholm integral equation of the second kind.

Keywords: nonlocal problem, operators of fractional integrodifferentiation, Cauchy problem, singular equation, Fredholm integral equation.

UDC: 517.946

Received: 01.03.2016