Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus
This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary-value problems for differential equations of fractional order. In particular, we show the positive definiteness of studying operators, which makes it possible to select areas in the comple...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4327 |
| _version_ | 1797573101283704832 |
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| author | Tatiana Matseevich Temirkhan Aleroev |
| author_facet | Tatiana Matseevich Temirkhan Aleroev |
| author_sort | Tatiana Matseevich |
| collection | DOAJ |
| description | This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary-value problems for differential equations of fractional order. In particular, we show the positive definiteness of studying operators, which makes it possible to select areas in the complex plane where there are no eigenvalues for these operators. |
| first_indexed | 2024-03-10T21:04:52Z |
| format | Article |
| id | doaj.art-98f10be24f014bf59218e6a5aedfdf65 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:52Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-98f10be24f014bf59218e6a5aedfdf652023-11-19T17:14:26ZengMDPI AGMathematics2227-73902023-10-011120432710.3390/math11204327Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional CalculusTatiana Matseevich0Temirkhan Aleroev1Department of Higher Mathematics, National Research Moscow State Civil Engineering University, 26, Yaroslavskoye Shosse, 129337 Moscow, RussiaDepartment of Higher Mathematics, National Research Moscow State Civil Engineering University, 26, Yaroslavskoye Shosse, 129337 Moscow, RussiaThis paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary-value problems for differential equations of fractional order. In particular, we show the positive definiteness of studying operators, which makes it possible to select areas in the complex plane where there are no eigenvalues for these operators.https://www.mdpi.com/2227-7390/11/20/4327fractional derivativeeigenvalueeigenfunctionMittag–Leffler functionspectral analysis |
| spellingShingle | Tatiana Matseevich Temirkhan Aleroev Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus Mathematics fractional derivative eigenvalue eigenfunction Mittag–Leffler function spectral analysis |
| title | Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus |
| title_full | Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus |
| title_fullStr | Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus |
| title_full_unstemmed | Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus |
| title_short | Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus |
| title_sort | spectral analysis of one class of positive definite operators and their application in fractional calculus |
| topic | fractional derivative eigenvalue eigenfunction Mittag–Leffler function spectral analysis |
| url | https://www.mdpi.com/2227-7390/11/20/4327 |
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