On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2021-11-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/24622 |
| _version_ | 1811312910874443776 |
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| author | Yuxin Zhang Xiping Liu Mei Jia |
| author_facet | Yuxin Zhang Xiping Liu Mei Jia |
| author_sort | Yuxin Zhang |
| collection | DOAJ |
| description | In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results. |
| first_indexed | 2024-04-13T10:44:55Z |
| format | Article |
| id | doaj.art-89b936ca13ae42dcad765ce64a5a13fb |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-04-13T10:44:55Z |
| publishDate | 2021-11-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-89b936ca13ae42dcad765ce64a5a13fb2022-12-22T02:49:49ZengVilnius University PressNonlinear Analysis1392-51132335-89632021-11-0126610.15388/namc.2021.26.24622On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delayYuxin Zhang0Xiping Liu1Mei JiaUniversity of Shanghai for Science and TechnologyUniversity of Shanghai for Science and TechnologyIn this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results.https://www.journals.vu.lt/nonlinear-analysis/article/view/24622boundary value problempiecewise differential equationleft and right fractional derivativedelaydisturbance parameterfixed point theorem |
| spellingShingle | Yuxin Zhang Xiping Liu Mei Jia On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay Nonlinear Analysis boundary value problem piecewise differential equation left and right fractional derivative delay disturbance parameter fixed point theorem |
| title | On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay |
| title_full | On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay |
| title_fullStr | On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay |
| title_full_unstemmed | On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay |
| title_short | On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay |
| title_sort | on the boundary value problems of piecewise differential equations with left right fractional derivatives and delay |
| topic | boundary value problem piecewise differential equation left and right fractional derivative delay disturbance parameter fixed point theorem |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/24622 |
| work_keys_str_mv | AT yuxinzhang ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay AT xipingliu ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay AT meijia ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay |