Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a...

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Published inBoundary value problems Vol. 2022; no. 1; pp. 1 - 16
Main Author Yan, Debao
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 14.01.2022
Hindawi Limited
SpringerOpen
Subjects
Analysis
Approximations and Expansions
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Existence theorems
Fixed point theorem
Fixed points (mathematics)
Fractional differential equation
Integral boundary condition
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Singular boundary value problem
Fractional differential equation
34B16
Fixed point theorem
Singular boundary value problem
Integral boundary condition
34B10
34A08
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Abstract We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.
AbstractList We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at $t=0$ t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.
We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t=0, 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.
We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.
Abstract We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at t = 0 $t=0$ , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.
ArticleNumber 3
Author Yan, Debao
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CitedBy_id crossref_primary_10_1016_j_cjph_2022_04_015
crossref_primary_10_1155_2024_5554742
crossref_primary_10_11948_20220329
crossref_primary_10_3934_mbe_2023206
Cites_doi 10.1186/s13661-016-0572-0
10.1006/jmaa.1996.0456
10.18514/MMN.2014.511
10.1186/s13662-020-02549-5
10.1016/j.jmaa.2005.02.052
10.1155/2009/375486
10.1186/1687-1847-2013-213
10.1186/1687-2770-2012-73
10.1016/j.na.2009.03.030
10.1186/s13661-018-0941-y
10.1016/j.mcm.2012.06.024
10.1016/j.na.2007.08.042
10.1007/s12190-013-0689-6
10.1155/ADE/2006/90479
10.1186/s13662-020-02594-0
10.1186/s13661-019-1205-1
10.1186/1687-2770-2012-81
10.1016/j.jmaa.2010.04.034
10.1515/GMJ.2009.401
10.1007/s12190-012-0610-8
10.1016/j.na.2009.07.012
10.1186/s13662-015-0729-7
10.22436/jnsa.010.04.63
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Issue 1
Keywords Fractional differential equation
34B16
Fixed point theorem
Singular boundary value problem
Integral boundary condition
34B10
34A08
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Wang, Y., Xu, J.: Sobolev Space, Southeast University Press (2003) (in Chinese)
PodlubnyI.Fractional Differential Equations1999San DiegoAcademic Press0924.34008
MillerK.S.RossB.An Introduction to the Fractional Calculus and Differential Equations1993New YorkWiley0789.26002
XuX.JiangD.YuanC.Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equationsNonlinear Anal.20097146764688254870110.1016/j.na.2009.03.030
TariboonJ.SitthiwiratthamT.NtouyasS.K.Boundary value problems for a new class of three-point nonlocal Riemann–Liouville integral boundary conditionsAdv. Differ. Equ.20132013308986410.1186/1687-1847-2013-213
QiuT.BaiZ.Existence of positive solutions for singular fractional differential equationsElectron. J. Differ. Equ.200814624489011172.34313
LakshmikanthamV.VatsalaA.S.Basic theory of fractional differential equationsNonlinear Anal.200869826772682244636110.1016/j.na.2007.08.042
ZhaoY.SunS.HanZ.ZhangM.Positive solutions for boundary value problems of nonlinear fractional differential equationsAppl. Math. Comput.20112176950695827756851227.34011
ZhangS.Positive solutions for boundary value problems of nonlinear fractional differential equationsElectron. J. Differ. Equ.20062006221358010.1155/ADE/2006/90479
AhmadB.NtouyasS.K.AssolamiA.Caputo type fractional differential equations with nonlocal Riemann–Liouville integral boundary conditionsJ. Appl. Math. Comput.201341339350301712510.1007/s12190-012-0610-8
JleliM.SametB.On positive solutions for a class of singular nonlinear fractional differential equationsBound. Value Probl.20122012296088310.1186/1687-2770-2012-73
KilbasA.A.SrivastavaH.M.TrujilloJ.J.Theory of Fractional Differential Equations2006AmsterdamElsevier1092.45003
MatarM.M.On existence of positive solution for initial value problem of nonlinear fractional differential equations of orderActa Math. Univ. Comen.2015LXXXIV1515733164031340.34031
JiangD.YuanC.The positive properties of the Green function for Dirichlet type boundary value problems of nonlinear fractional differential equations and its applicationNonlinear Anal.201072710719257933910.1016/j.na.2009.07.012
KrasnoselskiiM.A.Two remarks on the method of successive approximationsUsp. Mat. Nauk19551012312768119
LiuL.MinD.WuY.Existence and multiplicity of positive solutions for a new class of singular higher-order fractional differential equations with Riemann–Stieltjes integral boundary value conditionsAdv. Differ. Equ.20202020414152110.1186/s13662-020-02594-0
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SamkoS.G.KilbasA.A.MarichevO.I.Fractional Integrals and Derivatives, Theory and Applications1993YverdonGordon & Breach0818.26003
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WangY.The Green function of a class of two-term fractional differential equation boundary value problem and its applicationAdv. Differ. Equ.20202020406780910.1186/s13662-020-02549-5
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AhmadB.SivasundaramS.On four point nonlocal boundary value problems of nonlinear integro-differential equations of fractional orderAppl. Math. Comput.201021748048726785591207.45014
DarwishM.A.NtouyasS.K.Existence results for first order boundary value problems for fractional differential equations with four-point integral boundary conditionsMiskolc Math. Notes20141515161325966910.18514/MMN.2014.511
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WangY.LiuL.Positive properties of the Green function for two-term fractional differential equations and its applicationsJ. Nonlinear Sci. Appl.20171020942102364663810.22436/jnsa.010.04.63
HeY.Existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditionsAdv. Differ. Equ.20162016345408610.1186/s13662-015-0729-7
DelboscoD.RodinoL.Existence and uniqueness for a nonlinear fractional differential equationJ. Math. Anal. Appl.1996204609625142146710.1006/jmaa.1996.0456
WuJ.LiuY.Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spacesElectron. J. Differ. Equ.20092009255009110.1155/2009/375486
YanD.Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with singular boundary value conditionsMath. Probl. Eng.202120214241894
BaiZ.LiuH.Positive solutions for boundary value problem of nonlinear fractional differential equationJ. Math. Anal. Appl.20053112495505216841310.1016/j.jmaa.2005.02.052
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WangY.Existence and multiplicity of positive solutions for a class of singular fractional nonlocal boundary value problemsBound. Value Probl.20192019395078010.1186/s13661-019-1205-1
ZhangX.ZhongQ.Multiple positive solutions for nonlocal boundary value problems of singular fractional differential equationsBound. Value Probl.20162016347674310.1186/s13661-016-0572-0
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MinD.LiuL.WuY.Uniqueness of positive solutions for the singular nonlinear fractional differential equations involving integral boundary value conditionsBound. Value Probl.2018201810.1186/s13661-018-0941-y
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A.A. Kilbas (1585_CR1) 2006
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D. Jiang (1585_CR11) 2010; 72
Y. Wang (1585_CR18) 2017; 10
Y. Wang (1585_CR33) 2019; 2019
S. Vong (1585_CR32) 2013; 57
D. Min (1585_CR30) 2018; 2018
R.P. Agarwal (1585_CR24) 2010; 371
D. Yan (1585_CR28) 2021; 2021
Y. He (1585_CR29) 2016; 2016
B. Ahmad (1585_CR17) 2013; 41
Z. Bai (1585_CR9) 2005; 311
V. Lakshmikantham (1585_CR5) 2007; 11
M. Jleli (1585_CR26) 2012; 2012
D.R. Smart (1585_CR35) 1980
D. Delbosco (1585_CR12) 1996; 204
L. Guo (1585_CR27) 2014; 44
Y. Wang (1585_CR22) 2012; 2012
R.P. Agarwal (1585_CR8) 2009; 16
M.M. Matar (1585_CR20) 2015; LXXXIV
S.G. Samko (1585_CR6) 1993
X. Xu (1585_CR13) 2009; 71
1585_CR36
M.A. Darwish (1585_CR16) 2014; 15
Y. Wang (1585_CR19) 2020; 2020
S. Zhang (1585_CR7) 2006; 2006
V. Lakshmikantham (1585_CR4) 2008; 69
X. Zhang (1585_CR23) 2016; 2016
Y. Zhao (1585_CR21) 2011; 217
References_xml – reference: MinD.LiuL.WuY.Uniqueness of positive solutions for the singular nonlinear fractional differential equations involving integral boundary value conditionsBound. Value Probl.2018201810.1186/s13661-018-0941-y
– reference: LakshmikanthamV.VatsalaA.S.Basic theory of fractional differential equationsNonlinear Anal.200869826772682244636110.1016/j.na.2007.08.042
– reference: AhmadB.NtouyasS.K.AssolamiA.Caputo type fractional differential equations with nonlocal Riemann–Liouville integral boundary conditionsJ. Appl. Math. Comput.201341339350301712510.1007/s12190-012-0610-8
– reference: SmartD.R.Fixed Point Theorems1980CambridgeCambridge University Press0427.47036
– reference: HeY.Existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditionsAdv. Differ. Equ.20162016345408610.1186/s13662-015-0729-7
– reference: YanD.Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with singular boundary value conditionsMath. Probl. Eng.202120214241894
– reference: DelboscoD.RodinoL.Existence and uniqueness for a nonlinear fractional differential equationJ. Math. Anal. Appl.1996204609625142146710.1006/jmaa.1996.0456
– reference: WangY.The Green function of a class of two-term fractional differential equation boundary value problem and its applicationAdv. Differ. Equ.20202020406780910.1186/s13662-020-02549-5
– reference: PodlubnyI.Fractional Differential Equations1999San DiegoAcademic Press0924.34008
– reference: WuJ.LiuY.Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spacesElectron. J. Differ. Equ.20092009255009110.1155/2009/375486
– reference: AgarwalR.P.BenchoraM.HamaniS.Boundary value problems for fractional differential equationsGeorgian Math. J.2009163401411257266310.1515/GMJ.2009.401
– reference: JiangD.YuanC.The positive properties of the Green function for Dirichlet type boundary value problems of nonlinear fractional differential equations and its applicationNonlinear Anal.201072710719257933910.1016/j.na.2009.07.012
– reference: WangY.LiuL.Positive properties of the Green function for two-term fractional differential equations and its applicationsJ. Nonlinear Sci. Appl.20171020942102364663810.22436/jnsa.010.04.63
– reference: LiuL.MinD.WuY.Existence and multiplicity of positive solutions for a new class of singular higher-order fractional differential equations with Riemann–Stieltjes integral boundary value conditionsAdv. Differ. Equ.20202020414152110.1186/s13662-020-02594-0
– reference: VongS.Positive solutions of singular fractional differential equation with integral boundary conditionsMath. Comput. Model.20135710531059303411010.1016/j.mcm.2012.06.024
– reference: KilbasA.A.SrivastavaH.M.TrujilloJ.J.Theory of Fractional Differential Equations2006AmsterdamElsevier1092.45003
– reference: WangY.LiuL.WuY.Existence and uniqueness of a positive solution to singular fractional differential equationsBound. Value Probl.20122012301633010.1186/1687-2770-2012-81
– reference: ZhaoY.SunS.HanZ.ZhangM.Positive solutions for boundary value problems of nonlinear fractional differential equationsAppl. Math. Comput.20112176950695827756851227.34011
– reference: ZhangS.Positive solutions for boundary value problems of nonlinear fractional differential equationsElectron. J. Differ. Equ.20062006221358010.1155/ADE/2006/90479
– reference: MillerK.S.RossB.An Introduction to the Fractional Calculus and Differential Equations1993New YorkWiley0789.26002
– reference: Wang, Y., Xu, J.: Sobolev Space, Southeast University Press (2003) (in Chinese)
– reference: KrasnoselskiiM.A.Two remarks on the method of successive approximationsUsp. Mat. Nauk19551012312768119
– reference: SamkoS.G.KilbasA.A.MarichevO.I.Fractional Integrals and Derivatives, Theory and Applications1993YverdonGordon & Breach0818.26003
– reference: GuoL.ZhangX.Existence of positive solutions for the singular fractional differential equationsJ. Appl. Math. Comput.201444215228314773810.1007/s12190-013-0689-6
– reference: DarwishM.A.NtouyasS.K.Existence results for first order boundary value problems for fractional differential equations with four-point integral boundary conditionsMiskolc Math. Notes20141515161325966910.18514/MMN.2014.511
– reference: AgarwalR.P.O’reganD.StaněkS.Positive solutions for Dirichlet problems of singular nonlinear fractional differential equationsJ. Math. Anal. Appl.20103715768266098610.1016/j.jmaa.2010.04.034
– reference: BaiZ.LiuH.Positive solutions for boundary value problem of nonlinear fractional differential equationJ. Math. Anal. Appl.20053112495505216841310.1016/j.jmaa.2005.02.052
– reference: WangY.Existence and multiplicity of positive solutions for a class of singular fractional nonlocal boundary value problemsBound. Value Probl.20192019395078010.1186/s13661-019-1205-1
– reference: TariboonJ.SitthiwiratthamT.NtouyasS.K.Boundary value problems for a new class of three-point nonlocal Riemann–Liouville integral boundary conditionsAdv. Differ. Equ.20132013308986410.1186/1687-1847-2013-213
– reference: ZhangX.ZhongQ.Multiple positive solutions for nonlocal boundary value problems of singular fractional differential equationsBound. Value Probl.20162016347674310.1186/s13661-016-0572-0
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Snippet We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear...
Abstract We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the...
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SubjectTerms Analysis
Approximations and Expansions
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Existence theorems
Fixed point theorem
Fixed points (mathematics)
Fractional differential equation
Integral boundary condition
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Singular boundary value problem
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Title Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions
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