Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives
In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsi...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
De Gruyter
2016-06-01
|
Series: | Nonautonomous Dynamical Systems |
Subjects: | |
Online Access: | http://www.degruyter.com/view/j/msds.2016.3.issue-1/msds-2016-0004/msds-2016-0004.xml?format=INT |
_version_ | 1819199314679824384 |
---|---|
author | Liu Yuji |
author_facet | Liu Yuji |
author_sort | Liu Yuji |
collection | DOAJ |
description | In this article, we present a new method for converting the boundary value problems for impulsive
fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some
existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential
systems at resonance case and non-resonance case are established respectively. Our analysis relies on
the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate
main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear
impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19],
[Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance,
J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential
equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80]. |
first_indexed | 2024-12-23T03:14:22Z |
format | Article |
id | doaj.art-17f2f25982b24470b55db9b7e1a32f68 |
institution | Directory Open Access Journal |
issn | 2353-0626 |
language | English |
last_indexed | 2024-12-23T03:14:22Z |
publishDate | 2016-06-01 |
publisher | De Gruyter |
record_format | Article |
series | Nonautonomous Dynamical Systems |
spelling | doaj.art-17f2f25982b24470b55db9b7e1a32f682022-12-21T18:02:10ZengDe GruyterNonautonomous Dynamical Systems2353-06262016-06-0131428410.1515/msds-2016-0004msds-2016-0004Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivativesLiu Yuji0Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou 510000, P.R.ChinaIn this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].http://www.degruyter.com/view/j/msds.2016.3.issue-1/msds-2016-0004/msds-2016-0004.xml?format=INTimpulsive fractional differential system boundary value problem Schauder’s fixed point theorem coincidence degree |
spellingShingle | Liu Yuji Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives Nonautonomous Dynamical Systems impulsive fractional differential system boundary value problem Schauder’s fixed point theorem coincidence degree |
title | Studies on BVPs for IFDEs involved with the
Riemann-Liouville type fractional derivatives |
title_full | Studies on BVPs for IFDEs involved with the
Riemann-Liouville type fractional derivatives |
title_fullStr | Studies on BVPs for IFDEs involved with the
Riemann-Liouville type fractional derivatives |
title_full_unstemmed | Studies on BVPs for IFDEs involved with the
Riemann-Liouville type fractional derivatives |
title_short | Studies on BVPs for IFDEs involved with the
Riemann-Liouville type fractional derivatives |
title_sort | studies on bvps for ifdes involved with the riemann liouville type fractional derivatives |
topic | impulsive fractional differential system boundary value problem Schauder’s fixed point theorem coincidence degree |
url | http://www.degruyter.com/view/j/msds.2016.3.issue-1/msds-2016-0004/msds-2016-0004.xml?format=INT |
work_keys_str_mv | AT liuyuji studiesonbvpsforifdesinvolvedwiththeriemannliouvilletypefractionalderivatives |