The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems
Abstract In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer substitution. That is, the nth eigenfunction ha...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-021-01556-z |
| _version_ | 1818587415071162368 |
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| author | Yan-Hsiou Cheng |
| author_facet | Yan-Hsiou Cheng |
| author_sort | Yan-Hsiou Cheng |
| collection | DOAJ |
| description | Abstract In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer substitution. That is, the nth eigenfunction has n − 1 $n-1$ zero in ( 0 , π ) $( 0,\pi ) $ for n ∈ N $n\in \mathbb{N}$ . Then, using the homotopy argument, we find the minimum of the first eigenvalue gap under the class of single-well potential functions and the first eigenvalue ratio under the class of single-barrier density functions. The result of the eigenvalue gap is different from the classical Sturm–Liouville problem. |
| first_indexed | 2024-12-16T09:08:29Z |
| format | Article |
| id | doaj.art-c7ab39c6aaef485abe6e1a0b33681049 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-16T09:08:29Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-c7ab39c6aaef485abe6e1a0b336810492022-12-21T22:37:02ZengSpringerOpenBoundary Value Problems1687-27702021-09-012021111010.1186/s13661-021-01556-zThe dual eigenvalue problems of the conformable fractional Sturm–Liouville problemsYan-Hsiou Cheng0Department of Mathematics and Information Education, National Taipei University of EducationAbstract In this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer substitution. That is, the nth eigenfunction has n − 1 $n-1$ zero in ( 0 , π ) $( 0,\pi ) $ for n ∈ N $n\in \mathbb{N}$ . Then, using the homotopy argument, we find the minimum of the first eigenvalue gap under the class of single-well potential functions and the first eigenvalue ratio under the class of single-barrier density functions. The result of the eigenvalue gap is different from the classical Sturm–Liouville problem.https://doi.org/10.1186/s13661-021-01556-zConformable fractional derivativesSturm–Liouville problemEigenvalue gapEigenvalue ratio |
| spellingShingle | Yan-Hsiou Cheng The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems Boundary Value Problems Conformable fractional derivatives Sturm–Liouville problem Eigenvalue gap Eigenvalue ratio |
| title | The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems |
| title_full | The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems |
| title_fullStr | The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems |
| title_full_unstemmed | The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems |
| title_short | The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems |
| title_sort | dual eigenvalue problems of the conformable fractional sturm liouville problems |
| topic | Conformable fractional derivatives Sturm–Liouville problem Eigenvalue gap Eigenvalue ratio |
| url | https://doi.org/10.1186/s13661-021-01556-z |
| work_keys_str_mv | AT yanhsioucheng thedualeigenvalueproblemsoftheconformablefractionalsturmliouvilleproblems AT yanhsioucheng dualeigenvalueproblemsoftheconformablefractionalsturmliouvilleproblems |