A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution
A two-point boundary value problem on the interval [0, 1] is considered, where the highest-order derivative is a Caputo fractional derivative of order 2 − δ with 0 < δ < 1. A necessary and sufficient condition for existence and uniqueness of a solution u is derived. For this solution the...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yaroslavl State University
2016-06-01
|
| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/352 |
| _version_ | 1797877861177098240 |
|---|---|
| author | M. Stynes |
| author_facet | M. Stynes |
| author_sort | M. Stynes |
| collection | DOAJ |
| description | A two-point boundary value problem on the interval [0, 1] is considered, where the highest-order derivative is a Caputo fractional derivative of order 2 − δ with 0 < δ < 1. A necessary and sufficient condition for existence and uniqueness of a solution u is derived. For this solution the derivative uŐ is absolutely continuous on [0, 1]. It is shown that if one assumes more regularity — that u lies in C2[0, 1] — then this places a subtle restriction on the data of the problem. |
| first_indexed | 2024-04-10T02:23:53Z |
| format | Article |
| id | doaj.art-2ed386cb7e464e248818613694ff0682 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-10T02:23:53Z |
| publishDate | 2016-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-2ed386cb7e464e248818613694ff06822023-03-13T08:07:34ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172016-06-0123337037610.18255/1818-1015-2016-3-370-376309A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a SolutionM. Stynes0Пекинский Исследовательский Центр Вычислительных Наук, район Хайдянь, Пекин 100193, КитайA two-point boundary value problem on the interval [0, 1] is considered, where the highest-order derivative is a Caputo fractional derivative of order 2 − δ with 0 < δ < 1. A necessary and sufficient condition for existence and uniqueness of a solution u is derived. For this solution the derivative uŐ is absolutely continuous on [0, 1]. It is shown that if one assumes more regularity — that u lies in C2[0, 1] — then this places a subtle restriction on the data of the problem.https://www.mais-journal.ru/jour/article/view/352дробная производнаякраевая задачасуществованиеединственностьрегулярность |
| spellingShingle | M. Stynes A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution Моделирование и анализ информационных систем дробная производная краевая задача существование единственность регулярность |
| title | A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution |
| title_full | A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution |
| title_fullStr | A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution |
| title_full_unstemmed | A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution |
| title_short | A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution |
| title_sort | caputo two point boundary value problem existence uniqueness and regularity of a solution |
| topic | дробная производная краевая задача существование единственность регулярность |
| url | https://www.mais-journal.ru/jour/article/view/352 |
| work_keys_str_mv | AT mstynes acaputotwopointboundaryvalueproblemexistenceuniquenessandregularityofasolution AT mstynes caputotwopointboundaryvalueproblemexistenceuniquenessandregularityofasolution |