Analysis of some Katugampola fractional differential equations with fractional boundary conditions
In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2021359?viewType=HTML |
| _version_ | 1818837204792770560 |
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| author | Barbara Łupińska Ewa Schmeidel |
| author_facet | Barbara Łupińska Ewa Schmeidel |
| author_sort | Barbara Łupińska |
| collection | DOAJ |
| description | In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results. |
| first_indexed | 2024-12-19T03:18:47Z |
| format | Article |
| id | doaj.art-135385de037f4432b47c41ffef15cc43 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-19T03:18:47Z |
| publishDate | 2021-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-135385de037f4432b47c41ffef15cc432022-12-21T20:37:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-08-011867269727910.3934/mbe.2021359Analysis of some Katugampola fractional differential equations with fractional boundary conditionsBarbara Łupińska0Ewa Schmeidel1Institute of Computer Science, University of Bialystok, Konstantego Ciołkowskiego 1M, 15-245 Białystok, PolandInstitute of Computer Science, University of Bialystok, Konstantego Ciołkowskiego 1M, 15-245 Białystok, PolandIn this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.https://www.aimspress.com/article/doi/10.3934/mbe.2021359?viewType=HTMLfractional calculuslyapunov inequalitygreen functionfractional differential equationskatugampola derivativeeigenvalue of fractional differential equation |
| spellingShingle | Barbara Łupińska Ewa Schmeidel Analysis of some Katugampola fractional differential equations with fractional boundary conditions Mathematical Biosciences and Engineering fractional calculus lyapunov inequality green function fractional differential equations katugampola derivative eigenvalue of fractional differential equation |
| title | Analysis of some Katugampola fractional differential equations with fractional boundary conditions |
| title_full | Analysis of some Katugampola fractional differential equations with fractional boundary conditions |
| title_fullStr | Analysis of some Katugampola fractional differential equations with fractional boundary conditions |
| title_full_unstemmed | Analysis of some Katugampola fractional differential equations with fractional boundary conditions |
| title_short | Analysis of some Katugampola fractional differential equations with fractional boundary conditions |
| title_sort | analysis of some katugampola fractional differential equations with fractional boundary conditions |
| topic | fractional calculus lyapunov inequality green function fractional differential equations katugampola derivative eigenvalue of fractional differential equation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2021359?viewType=HTML |
| work_keys_str_mv | AT barbarałupinska analysisofsomekatugampolafractionaldifferentialequationswithfractionalboundaryconditions AT ewaschmeidel analysisofsomekatugampolafractionaldifferentialequationswithfractionalboundaryconditions |