On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In...
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doaj-8065a26df18d4d5f9a79889c65fc42792020-11-25T00:52:55ZengMDPI AGAxioms2075-16802019-10-018411710.3390/axioms8040117axioms8040117On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional OrderTemirkhan Aleroev0NRU MGSU, Moscow 129337, RussiaThe present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, a study of the completeness of systems of eigenfunctions and associated functions has begun relatively recently. In this paper, the completeness of the system of eigenfunctions and associated functions of one class of non-self-adjoint integral operators corresponding boundary value problems for fractional differential equations is established. The proof is based on the well-known Theorem of M.S. Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. The results of Dzhrbashian-Nersesian on the asymptotics of the zeros of the Mittag-Leffler function are used.https://www.mdpi.com/2075-1680/8/4/117mittag-leffler functionspectrumeigenvaluefractional derivative |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Temirkhan Aleroev |
spellingShingle |
Temirkhan Aleroev On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order Axioms mittag-leffler function spectrum eigenvalue fractional derivative |
author_facet |
Temirkhan Aleroev |
author_sort |
Temirkhan Aleroev |
title |
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order |
title_short |
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order |
title_full |
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order |
title_fullStr |
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order |
title_full_unstemmed |
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order |
title_sort |
on one problems of spectral theory for ordinary differential equations of fractional order |
publisher |
MDPI AG |
series |
Axioms |
issn |
2075-1680 |
publishDate |
2019-10-01 |
description |
The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, a study of the completeness of systems of eigenfunctions and associated functions has begun relatively recently. In this paper, the completeness of the system of eigenfunctions and associated functions of one class of non-self-adjoint integral operators corresponding boundary value problems for fractional differential equations is established. The proof is based on the well-known Theorem of M.S. Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. The results of Dzhrbashian-Nersesian on the asymptotics of the zeros of the Mittag-Leffler function are used. |
topic |
mittag-leffler function spectrum eigenvalue fractional derivative |
url |
https://www.mdpi.com/2075-1680/8/4/117 |
work_keys_str_mv |
AT temirkhanaleroev ononeproblemsofspectraltheoryforordinarydifferentialequationsoffractionalorder |
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1725240171105878016 |