Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations
In this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite i...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-03-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/3/148 |
| _version_ | 1797241003947589632 |
|---|---|
| author | Leila Gholizadeh Zivlaei Angelo B. Mingarelli |
| author_facet | Leila Gholizadeh Zivlaei Angelo B. Mingarelli |
| author_sort | Leila Gholizadeh Zivlaei |
| collection | DOAJ |
| description | In this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite interval under consideration. The results are valid for equations that have sign-indefinite leading terms and measurable coefficients. Existence and uniqueness theorem results are also provided for two-point boundary value problems in a closed interval. |
| first_indexed | 2024-04-24T18:16:25Z |
| format | Article |
| id | doaj.art-f3b589f7a2704327a5f64ccdd348698b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-04-24T18:16:25Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f3b589f7a2704327a5f64ccdd348698b2024-03-27T13:42:04ZengMDPI AGFractal and Fractional2504-31102024-03-018314810.3390/fractalfract8030148Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville EquationsLeila Gholizadeh Zivlaei0Angelo B. Mingarelli1School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, CanadaSchool of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, CanadaIn this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite interval under consideration. The results are valid for equations that have sign-indefinite leading terms and measurable coefficients. Existence and uniqueness theorem results are also provided for two-point boundary value problems in a closed interval.https://www.mdpi.com/2504-3110/8/3/148Riemann–LiouvilleCaputoSturm–Liouvillefractionalexistenceuniqueness |
| spellingShingle | Leila Gholizadeh Zivlaei Angelo B. Mingarelli Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations Fractal and Fractional Riemann–Liouville Caputo Sturm–Liouville fractional existence uniqueness |
| title | Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations |
| title_full | Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations |
| title_fullStr | Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations |
| title_full_unstemmed | Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations |
| title_short | Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations |
| title_sort | existence and uniqueness of some unconventional fractional sturm liouville equations |
| topic | Riemann–Liouville Caputo Sturm–Liouville fractional existence uniqueness |
| url | https://www.mdpi.com/2504-3110/8/3/148 |
| work_keys_str_mv | AT leilagholizadehzivlaei existenceanduniquenessofsomeunconventionalfractionalsturmliouvilleequations AT angelobmingarelli existenceanduniquenessofsomeunconventionalfractionalsturmliouvilleequations |