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; Mukhamed Aleroev; Hedi Aleroeva; Temirkhan Aleroev

doi:10.3934/math.2019.3.714

AIMS Mathematics

2019, Volume 4, Issue 3: 714-720. doi: 10.3934/math.2019.3.714

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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

Received: 21 April 2019 Accepted: 12 June 2019 Published: 20 June 2019
MSC : 26A33, 34A08

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.
- 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[J]. AIMS Mathematics, 2019, 4(3): 714-720. doi: 10.3934/math.2019.3.714

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Abstract

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.

References

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