On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems
In this paper, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1<δ<2. We first transform the problem to an equivalent system of equations, including integer and fr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2016-01-01
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| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364715000440 |
| _version_ | 1811254851779166208 |
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| author | Arwa Ba Abdulla Mohammed Al-Refai Ahmed Al-Rawashdeh |
| author_facet | Arwa Ba Abdulla Mohammed Al-Refai Ahmed Al-Rawashdeh |
| author_sort | Arwa Ba Abdulla |
| collection | DOAJ |
| description | In this paper, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1<δ<2. We first transform the problem to an equivalent system of equations, including integer and fractional derivatives. We then implement the method of upper and lower solutions to establish existence and uniqueness results to the resulting system. At the end, some examples are presented to illustrate the validity of our results. |
| first_indexed | 2024-04-12T17:13:58Z |
| format | Article |
| id | doaj.art-4fcbd11dbe314ca890725fe47eddcbe1 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-04-12T17:13:58Z |
| publishDate | 2016-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-4fcbd11dbe314ca890725fe47eddcbe12022-12-22T03:23:43ZengElsevierJournal of King Saud University: Science1018-36472016-01-0128110311010.1016/j.jksus.2015.05.001On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problemsArwa Ba AbdullaMohammed Al-RefaiAhmed Al-RawashdehIn this paper, we extend the maximum principle and the method of upper and lower solutions to study a class of nonlinear fractional boundary value problems with the Caputo fractional derivative 1<δ<2. We first transform the problem to an equivalent system of equations, including integer and fractional derivatives. We then implement the method of upper and lower solutions to establish existence and uniqueness results to the resulting system. At the end, some examples are presented to illustrate the validity of our results.http://www.sciencedirect.com/science/article/pii/S1018364715000440Fractional differential equationsBoundary value problemsMaximum principleLower and upper solutionsCaputo fractional derivative |
| spellingShingle | Arwa Ba Abdulla Mohammed Al-Refai Ahmed Al-Rawashdeh On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems Journal of King Saud University: Science Fractional differential equations Boundary value problems Maximum principle Lower and upper solutions Caputo fractional derivative |
| title | On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems |
| title_full | On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems |
| title_fullStr | On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems |
| title_full_unstemmed | On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems |
| title_short | On the existence and uniqueness of solutions for a class of non-linear fractional boundary value problems |
| title_sort | on the existence and uniqueness of solutions for a class of non linear fractional boundary value problems |
| topic | Fractional differential equations Boundary value problems Maximum principle Lower and upper solutions Caputo fractional derivative |
| url | http://www.sciencedirect.com/science/article/pii/S1018364715000440 |
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