This article is cited in 20 papers

Differential Equations

Problem with shift for the third-order equation with discontinuous coefficients

O. A. Repin^ab, S. K. Kumykova<sup>c

a</sup> Samara State Technical University, Samara, Russia
^b Samara State Economic University, Samara, Russia
^c Kabardino-Balkar State University, Nalchik, Russia

Abstract: The unique solvability of boundary value problem with Saigo operators for the third-order equation with multiple characteristics was investigated. The uniqueness theorem with constraints of inequality type on the known functions and different orders of generalized fractional integro-differentiation was proved. The existence of solution is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Keywords: boundary value problem, Gauss hypergeometric function, operators of fractional order, Fredholm equation.

UDC: 517.956.6+517.968.23

MSC: Primary 35M12; Secondary 26A33, 33C05

Original article submitted 17/X/2012
revision submitted – 16/XI/2012

DOI: 10.14498/vsgtu1123

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