Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses
Abstract In this paper, we mainly consider the existence and finite-time stability of solutions for a kind of ψ-Hilfer fractional differential equations involving time-varying delays and non-instantaneous impulses. By Schauder’s fixed point theorem, the contraction mapping principle and the Lagrange...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2101-9 |
| _version_ | 1811331622813827072 |
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| author | Danfeng Luo Zhiguo Luo |
| author_facet | Danfeng Luo Zhiguo Luo |
| author_sort | Danfeng Luo |
| collection | DOAJ |
| description | Abstract In this paper, we mainly consider the existence and finite-time stability of solutions for a kind of ψ-Hilfer fractional differential equations involving time-varying delays and non-instantaneous impulses. By Schauder’s fixed point theorem, the contraction mapping principle and the Lagrange mean-value theorem, we present new constructive results as regards existence and uniqueness of solutions. In addition, under some new criteria and by applying the generalized Gronwall inequality, we deduce that the solutions of the addressed equation have finite-time stability. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results. |
| first_indexed | 2024-04-13T16:23:27Z |
| format | Article |
| id | doaj.art-d737de6dae134d38a82879b45f2c117e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T16:23:27Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-d737de6dae134d38a82879b45f2c117e2022-12-22T02:39:49ZengSpringerOpenAdvances in Difference Equations1687-18472019-04-012019112110.1186/s13662-019-2101-9Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulsesDanfeng Luo0Zhiguo Luo1Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal UniversityKey Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal UniversityAbstract In this paper, we mainly consider the existence and finite-time stability of solutions for a kind of ψ-Hilfer fractional differential equations involving time-varying delays and non-instantaneous impulses. By Schauder’s fixed point theorem, the contraction mapping principle and the Lagrange mean-value theorem, we present new constructive results as regards existence and uniqueness of solutions. In addition, under some new criteria and by applying the generalized Gronwall inequality, we deduce that the solutions of the addressed equation have finite-time stability. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.http://link.springer.com/article/10.1186/s13662-019-2101-9ψ-Hilfer fractional differential equationExistenceFinite-time stabilityTime-varying delaysNon-instantaneous impulses |
| spellingShingle | Danfeng Luo Zhiguo Luo Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses Advances in Difference Equations ψ-Hilfer fractional differential equation Existence Finite-time stability Time-varying delays Non-instantaneous impulses |
| title | Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses |
| title_full | Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses |
| title_fullStr | Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses |
| title_full_unstemmed | Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses |
| title_short | Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses |
| title_sort | existence and finite time stability of solutions for a class of nonlinear fractional differential equations with time varying delays and non instantaneous impulses |
| topic | ψ-Hilfer fractional differential equation Existence Finite-time stability Time-varying delays Non-instantaneous impulses |
| url | http://link.springer.com/article/10.1186/s13662-019-2101-9 |
| work_keys_str_mv | AT danfengluo existenceandfinitetimestabilityofsolutionsforaclassofnonlinearfractionaldifferentialequationswithtimevaryingdelaysandnoninstantaneousimpulses AT zhiguoluo existenceandfinitetimestabilityofsolutionsforaclassofnonlinearfractionaldifferentialequationswithtimevaryingdelaysandnoninstantaneousimpulses |