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

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

Special Issues: Initial and Boundary Value Problems for Differential Equations

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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Keywords Mittag-Leffler function; spectrum; eigenvalue; fractional derivative; completeness

Citation: Mukhamed Aleroev, Hedi Aleroeva, Temirkhan Aleroev. Proof of the completeness of the system of eigenfunctions for one boundary-value problem for the fractional differential equation. AIMS Mathematics, 2019, 4(3): 714-720. doi: 10.3934/math.2019.3.714

References

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