On the solvability of nonlocal problem for a hyperbolic equation of the second kind

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 Chernyshevskii str., Nalchik, 360004 Russia

Abstract: In the characteristic triangle, for a hyperbolic equation of the second kind we study a nonlocal problem when boundary condition contains a linear combination of operators of fractional Riemann–Liouville integro-differentition. We establish intervals of change of orders of operators of fractional integro-differentiation associated with the parameters of the equation for which the problem is either uniquely solvable or has more than one solution.

Keywords: operators of fractional integro-differentiation, Volterra integral equation of the second kind, method of successive approximations.

UDC: 517.956

Received: 27.02.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:9, 46–52

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