This article is cited in 1 paper

Differential Equations

On the solvability of nonlocal problem with generalized operators M. Saigo for Bitsadze–Lykov equation

A. V. Tarasenko, I. P. Egorova

Samara State University of Architecture and Construction, Samara, 443001, Russian Federation

Abstract: A nonlocal boundary value problem for the equation of moisture transfer was studied in the field, which is the union of two characteristic triangles. The novelty of the formulation of the problem lies in the fact that the boundary conditions include operators of generalized of fractional integro-differentiation in the sense of M. Saigo. The uniqueness of the solution of the problem was proved using the extremum principle for hyperbolic equations. Properties of operators of generalized fractional integro-differentiation in the sense of M. Saigo were used in the proof. Existence of a solution is equivalent reduced to the solvability of a characteristic singular integral equation with Cauchy kernel for which the smoothness of the right-hand side was studied.

Keywords: boundary value problem, generalized operator of fractional integro-differentiation, integral equation with Cauchy kernel.

UDC: 517.956.6

MSC: 35М12, 35M10

Original article submitted 11/XI/2014
revision submitted – 09/XII/2014

DOI: 10.14498/vsgtu1363

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