Positive solutions for a system of semipositone coupled fractional boundary value problems

We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions.

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Published inBoundary value problems Vol. 2016; no. 1; pp. 1 - 23
Main Authors Henderson, Johnny, Luca, Rodica
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 08.03.2016
Hindawi Limited
Subjects
Analysis
Approximations and Expansions
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Integrals
Joining
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Special Collection in the honor of the Life and Research of Weigao Ge
positive solutions
Riemann-Liouville fractional differential equations
coupled integral boundary conditions
sign-changing nonlinearities
34A08
45G15
Online AccessGet full text

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Abstract We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions.
AbstractList We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to coupled integral boundary conditions.
ArticleNumber 61
Author Luca, Rodica
Henderson, Johnny
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  fullname: Henderson, Johnny
  organization: Department of Mathematics, Baylor University
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  givenname: Rodica
  surname: Luca
  fullname: Luca, Rodica
  email: rluca@math.tuiasi.ro
  organization: Department of Mathematics, Gh. Asachi Technical University
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Cites_doi 10.1017/CBO9780511543005
10.1016/j.amc.2014.10.028
10.2478/s13540-012-0036-x
10.2478/s13540-013-0061-4
10.1186/1687-2770-2014-60
10.1186/1687-1847-2014-179
10.1515/fca-2015-0024
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Issue 1
Keywords positive solutions
Riemann-Liouville fractional differential equations
coupled integral boundary conditions
sign-changing nonlinearities
34A08
45G15
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References YuanCJiangDO’ReganDAgarwalRPMultiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditionsElectron. J. Qual. Theory Differ. Equ.20122012288975510.1186/1687-1847-2012-1306476163
YuanCMultiple positive solutions for (n−1,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n-1,1)$\end{document}-type semipositone conjugate boundary value problems of nonlinear fractional differential equationsElectron. J. Qual. Theory Differ. Equ.2010201026520661210.34008
GraefJRKongLKongQWangMUniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditionsFract. Calc. Appl. Anal.2012153509528294411410.2478/s13540-012-0036-x1279.34007
HendersonJLucaRTudoracheAOn a system of fractional differential equations with coupled integral boundary conditionsFract. Calc. Appl. Anal.2015182361386332390710.1515/fca-2015-00241315.34012
HendersonJLucaRPositive solutions for a system of nonlocal fractional boundary value problemsFract. Calc. Appl. Anal.20131649851008312434810.2478/s13540-013-0061-41312.34015
SamkoSGKilbasAAMarichevOIFractional Integrals and Derivatives: Theory and Applications1993YverdonGordon & Breach0818.26003
LucaRTudoracheAPositive solutions to a system of semipositone fractional boundary value problemsAdv. Differ. Equ.20142014335733710.1186/1687-1847-2014-179
GuoDLakshmikanthamVNonlinear Problems in Abstract Cones1988New YorkAcademic Press0661.47045
KilbasAASrivastavaHMTrujilloJJTheory and Applications of Fractional Differential Equations2006AmsterdamElsevier10.1016/S0304-0208(06)80001-01092.45003
AgarwalRPMeehanMO’ReganDFixed Point Theory and Applications2001CambridgeCambridge University Press10.1017/CBO97805115430050960.54027
HendersonJLucaRPositive solutions for a system of fractional differential equations with coupled integral boundary conditionsAppl. Math. Comput.2014249182197327941210.1016/j.amc.2014.10.028
HendersonJLucaRExistence and multiplicity of positive solutions for a system of fractional boundary value problemsBound. Value Probl.20142014335263310.1186/1687-2770-2014-601307.34013
SabatierJAgrawalOPMachadoJATAdvances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering2007DordrechtSpringer1116.00014
DasSFunctional Fractional Calculus for System Identification and Controls2008New YorkSpringer1154.26007
PodlubnyIFractional Differential Equations1999San DiegoAcademic Press0924.34008
(569_CR5) 2007
JR Graef (569_CR2) 2012; 15
J Henderson (569_CR7) 2014; 249
J Henderson (569_CR10) 2014; 2014
I Podlubny (569_CR4) 1999
C Yuan (569_CR13) 2010; 2010
S Das (569_CR1) 2008
RP Agarwal (569_CR14) 2001
SG Samko (569_CR6) 1993
D Guo (569_CR15) 1988
R Luca (569_CR11) 2014; 2014
J Henderson (569_CR8) 2015; 18
J Henderson (569_CR9) 2013; 16
AA Kilbas (569_CR3) 2006
C Yuan (569_CR12) 2012; 2012
References_xml – reference: HendersonJLucaRPositive solutions for a system of fractional differential equations with coupled integral boundary conditionsAppl. Math. Comput.2014249182197327941210.1016/j.amc.2014.10.028
– reference: GuoDLakshmikanthamVNonlinear Problems in Abstract Cones1988New YorkAcademic Press0661.47045
– reference: HendersonJLucaRTudoracheAOn a system of fractional differential equations with coupled integral boundary conditionsFract. Calc. Appl. Anal.2015182361386332390710.1515/fca-2015-00241315.34012
– reference: SabatierJAgrawalOPMachadoJATAdvances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering2007DordrechtSpringer1116.00014
– reference: HendersonJLucaRExistence and multiplicity of positive solutions for a system of fractional boundary value problemsBound. Value Probl.20142014335263310.1186/1687-2770-2014-601307.34013
– reference: GraefJRKongLKongQWangMUniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditionsFract. Calc. Appl. Anal.2012153509528294411410.2478/s13540-012-0036-x1279.34007
– reference: PodlubnyIFractional Differential Equations1999San DiegoAcademic Press0924.34008
– reference: YuanCJiangDO’ReganDAgarwalRPMultiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditionsElectron. J. Qual. Theory Differ. Equ.20122012288975510.1186/1687-1847-2012-1306476163
– reference: AgarwalRPMeehanMO’ReganDFixed Point Theory and Applications2001CambridgeCambridge University Press10.1017/CBO97805115430050960.54027
– reference: SamkoSGKilbasAAMarichevOIFractional Integrals and Derivatives: Theory and Applications1993YverdonGordon & Breach0818.26003
– reference: KilbasAASrivastavaHMTrujilloJJTheory and Applications of Fractional Differential Equations2006AmsterdamElsevier10.1016/S0304-0208(06)80001-01092.45003
– reference: YuanCMultiple positive solutions for (n−1,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n-1,1)$\end{document}-type semipositone conjugate boundary value problems of nonlinear fractional differential equationsElectron. J. Qual. Theory Differ. Equ.2010201026520661210.34008
– reference: LucaRTudoracheAPositive solutions to a system of semipositone fractional boundary value problemsAdv. Differ. Equ.20142014335733710.1186/1687-1847-2014-179
– reference: HendersonJLucaRPositive solutions for a system of nonlocal fractional boundary value problemsFract. Calc. Appl. Anal.20131649851008312434810.2478/s13540-013-0061-41312.34015
– reference: DasSFunctional Fractional Calculus for System Identification and Controls2008New YorkSpringer1154.26007
– volume-title: Fractional Differential Equations
  year: 1999
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Snippet We study the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with sign-changing nonlinearities,...
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SubjectTerms Analysis
Approximations and Expansions
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Integrals
Joining
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Special Collection in the honor of the Life and Research of Weigao Ge
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Title Positive solutions for a system of semipositone coupled fractional boundary value problems
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