This article is cited in 3 papers

Differential Equations

On a class of nonlocal problems for hyperbolic equations with degeneration of type and order

O. A. Repin^ab, S. K. Kumykova<sup>c

a</sup> Samara State Technical University
^b Samara State University of Economics
^c Kabardino-Balkar State University, Nal'chik

Abstract: Nonlocal problems for the second order hyperbolic model equation were studied in the characteristic area. The type and order of equations degenerate on the same line $ y = 0 $. Nonlocal condition is given by means of fractional integro-differentiation of arbitrary order on the boundary. Nonlocal condition connects fractional derivatives and integrals of the desired solution. For different values of order operators of fractional integro-differentiation within the boundary condition the unique solvability of the considered problems was proved or non-uniqueness of the solution was estimated.

Keywords: nonlocal boundary value problem, fractional integro-differentiation operators, Cauchy problem, second kind Volterra integral equation, Abel integral equation.

UDC: 517.956.326

MSC: 35M12

Original article submitted 23/X/2014
revision submitted – 05/XI/2014

DOI: 10.14498/vsgtu1348

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