FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES
In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use bot...
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| Format: | Article |
| Language: | English |
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Gdańsk University of Technology
2016-01-01
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| Series: | TASK Quarterly |
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| Online Access: | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1853 |
| _version_ | 1811306816171147264 |
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| author | TADEUSZ JANKOWSKI |
| author_facet | TADEUSZ JANKOWSKI |
| author_sort | TADEUSZ JANKOWSKI |
| collection | DOAJ |
| description |
In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems are also discussed. A few examples illustrate the results.
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| first_indexed | 2024-04-13T08:52:32Z |
| format | Article |
| id | doaj.art-9af19d58584c49d3b3d62ff38a56c878 |
| institution | Directory Open Access Journal |
| issn | 1428-6394 |
| language | English |
| last_indexed | 2024-04-13T08:52:32Z |
| publishDate | 2016-01-01 |
| publisher | Gdańsk University of Technology |
| record_format | Article |
| series | TASK Quarterly |
| spelling | doaj.art-9af19d58584c49d3b3d62ff38a56c8782022-12-22T02:53:26ZengGdańsk University of TechnologyTASK Quarterly1428-63942016-01-0120110.17466/TQ2016/20.1/JFRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVESTADEUSZ JANKOWSKI0Gdansk University of Technology, Department of Differential Equations and Applied Mathematics In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems are also discussed. A few examples illustrate the results. https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1853right-handed Riemann-Liouville fractional derivativesnonlinear boundary problemslinear problemsexistence of solutionsMittag-Leffler functions |
| spellingShingle | TADEUSZ JANKOWSKI FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES TASK Quarterly right-handed Riemann-Liouville fractional derivatives nonlinear boundary problems linear problems existence of solutions Mittag-Leffler functions |
| title | FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES |
| title_full | FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES |
| title_fullStr | FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES |
| title_full_unstemmed | FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES |
| title_short | FRACTIONAL PROBLEMS WITH RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES |
| title_sort | fractional problems with right handed riemann liouville fractional derivatives |
| topic | right-handed Riemann-Liouville fractional derivatives nonlinear boundary problems linear problems existence of solutions Mittag-Leffler functions |
| url | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1853 |
| work_keys_str_mv | AT tadeuszjankowski fractionalproblemswithrighthandedriemannliouvillefractionalderivatives |