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AIMS Mathematics, 2019, 4(3): 714-720. doi: 10.3934/math.2019.3.714 Research article Special Issues

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Proof of the completeness of the system of eigenfunctions for one boundary-value problem for the fractional differential equation

Mukhamed Aleroev, Hedi Aleroeva, Temirkhan Aleroev

1 Department of Mathematical Methods and Computer Technologies, National Research University Higher School of Economics, Myasnitskaya st., 20, 101000, Moscow, Russia
2 Department of Informational Technologies, Moscow Technical University of Communications and Informatics, Aviamotornaya st. 8, 111024, Moscow, Russia
3 Department of Applied Mathematics , National Research Moscow State University of Civil Engineering, Yaroslavskoye highway 26, 129337, Moscow, Russia

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Special Issues: Initial and Boundary Value Problems for Differential Equations

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The present paper is devoted to the spectral analysis of operators induced by differential expressions of fractional order and boundary conditions of Sturm-Liouville type. In particular, this paper establishes the completeness of the system of eigenfunctions and associated functions of one class for non-self-adjoint integral operators associated with boundary-value problems for fractional-order differential equations.

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