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...

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Main Author: Liu Yuji
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
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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].
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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