This article is cited in 1 paper

Differential Equations and Mathematical Physics

Nonlocal problem for partial differential equations of fractional order

O. A. Repin^ab, A. V. Tarasenko<sup>c

a</sup> Samara State University of Economics, Samara, 443090, Russian Federation
^b Samara State Technical University, Samara, 443100, Russian Federation
^c Samara State University of Architecture and Construction, Samara, 443001, Russian Federation

Abstract: A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind.

Keywords: operator of fractional integro-differentiation, boundary value problem, Fredholm integral equation of the second kind.

UDC: 517.956.6

MSC: 35M12

Original article submitted 05/XI/2014
revision submitted – 11/I/2015

DOI: 10.14498/vsgtu1398

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