Discrete Fractional Boundary Value Problems and Inequalities

In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allow...

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Published inFractional calculus & applied analysis Vol. 24; no. 6; pp. 1777 - 1796
Main Authors Bohner, Martin, Fewster-Young, Nick
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2021
De Gruyter
Nature Publishing Group
Subjects
39A12
39A27
39A70
Abstract Harmonic Analysis
Analysis
boundary value problem
Boundary value problems
discrete fractional calculus
discrete fractional inequalities
existence of solutions
Existence theorems
Fixed points (mathematics)
Functional Analysis
Inequalities
Integral Transforms
Mathematics
Operational Calculus
Primary 26A33
Research Paper
Secondary 34A08
Primary 26A33
discrete fractional calculus
39A12
existence of solutions
39A27
boundary value problem
discrete fractional inequalities
39A70
Secondary 34A08
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Abstract In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer’s fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral representation, and, second, the establishment of solutions satisfying certain a priori bounds provided the key inequality holds. In order to establish the latter result, several novel discrete fractional inequalities are developed, each of them interesting in itself and of potential future use in different contexts. We illustrate the usefulness of our existence results by presenting two examples.
AbstractList In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral representation, and, second, the establishment of solutions satisfying certain bounds provided the key inequality holds. In order to establish the latter result, several novel discrete fractional inequalities are developed, each of them interesting in itself and of potential future use in different contexts. We illustrate the usefulness of our existence results by presenting two examples.
In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer’s fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral representation, and, second, the establishment of solutions satisfying certain a priori bounds provided the key inequality holds. In order to establish the latter result, several novel discrete fractional inequalities are developed, each of them interesting in itself and of potential future use in different contexts. We illustrate the usefulness of our existence results by presenting two examples.
In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral representation, and, second, the establishment of solutions satisfying certain a priori bounds provided the key inequality holds. In order to establish the latter result, several novel discrete fractional inequalities are developed, each of them interesting in itself and of potential future use in different contexts. We illustrate the usefulness of our existence results by presenting two examples.
Author Bohner, Martin
Fewster-Young, Nick
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10.1090/S0002-9947-1960-0124553-5
10.1515/fca-2019-0069
10.1016/j.cma.2004.06.006
10.1002/9783527626359
10.3906/mat-1904-29
10.1155/2020/6254013
10.1007/978-3-642-14574-2
10.1515/ms-2017-0422
10.1016/j.camwa.2011.11.029
10.26637/MJM0803/0017
10.2298/FIL1818339B
10.1002/mma.5869
10.1080/10236198.2019.1581180
10.4067/S0719-06462011000300009
10.3934/cpaa.2020269
10.1017/CBO9780511543005
10.1186/s13660-020-02485-8
10.1006/jmaa.2000.7194
10.1080/10236198.2018.1531129
10.1080/10236198.2018.1505882
10.1016/j.na.2007.08.042
10.1515/fca-2020-0051
10.1080/10236198.2017.1321641
10.1080/10236190903029241
10.1002/mma.6745
10.1016/j.na.2012.03.029
10.1007/978-3-319-25562-0
10.1216/RMJ-2019-49-8-2571
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Keywords Primary 26A33
discrete fractional calculus
39A12
existence of solutions
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boundary value problem
discrete fractional inequalities
39A70
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PublicationTitle Fractional calculus & applied analysis
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References AtιcιF MEloeP WTwo-point boundary value problems for finite fractional difference equationsJ. Difference Equ. Appl.2011174445456278335910.1080/10236190903029241
ChenCBohnerMJiaBExistence and uniqueness of solutions for nonlinear Caputo fractional difference equationsTurkish J. Math.2020443857869410048310.3906/mat-1904-29
GoodrichC SLyonsBVelcsovM TAnalytical and numerical monotonicity results for discrete fractional sequential differences with negative lower boundCommun. Pure Appl. Anal.2021201339358419150810.3934/cpaa.2020269
SelvamA G MAlzabutJDhineshbabuRRashidSRehmanMDiscrete fractional order two-point boundary value problem with some relevant physical applicationsJ. Inequal. Appl.2020202019415289810.1186/s13660-020-02485-8
Garić-DemirovićMMoranjkićSNurkanovićMNurkanovićZStability, Neimark–Sacker bifurcation, and approximation of the invariant curve of certain homogeneous second-order fractional difference equationDiscrete Dyn. Nat. Soc.2020202012413533410.1155/2020/6254013
PachpatteD BBagwanA SKhandagaleA DExistence of solutions to discrete boundary value problem of fractional difference equationsMalaya J. Mat.202083832837411260810.26637/MJM0803/0017
PratapARajaRCaoJHuangCNiezabitowskiMBagdasarOStability of discrete-time fractional-order time-delayed neural networks in complex fieldMath. Methods Appl. Sci.2021441419440418526210.1002/mma.6745
Fewster-YoungNTisdellC CThe existence of solutions to second-order singular boundary value problemsNonlinear Anal.2012751347984806292754510.1016/j.na.2012.03.029
CabadaADimitrovNNontrivial solutions of non-autonomous Dirichlet fractional discrete problemsFract. Calc. Appl. Anal.2020234980995415109410.1515/fca-2020-0051
AtιcιF MEloeP WGronwall’s inequality on discrete fractional calculusComput. Math. Appl.2012641031933200298934710.1016/j.camwa.2011.11.029
BohnerMStamovaI MAn impulsive delay discrete stochastic neural network fractional-order model and applications in financeFilomat2018321863396352389942210.2298/FIL1818339B
GoodrichC SSome new existence results for fractional difference equationsInt. J. Dyn. Syst. Differ. Equ.201131-214516227970461215.39004
HartmanPOn boundary value problems for systems of ordinary, nonlinear, second order differential equationsTrans. Amer. Math. Soc.19609649350912455310.1090/S0002-9947-1960-0124553-5
LakshmikanthamVVatsalaA STheory of fractional differential inequalities and applicationsCommun. Appl. Anal.2007113-439540223681911159.34006
ChenCBohnerMJiaBMethod of upper and lower solutions for nonlinear Caputo fractional difference equations and its applicationsFract. Calc. Appl. Anal.201922513071320404457610.1515/fca-2019-0069
GoodrichC SSolutions to a discrete right-focal fractional boundary value problemInt. J. Difference Equ.2010521952162771325
DiethelmKThe Analysis of Fractional Differential Equations2010WarsawVersita10.1007/978-3-642-14574-2
KilbasA ASrivastavaH MTrujilloJ JTheory and Applications of Fractional Differential Equations2006AmsterdamElsevier Science B.V1092.45003
LakshmikanthamVVatsalaA SBasic theory of fractional differential equationsNonlinear Anal.200869826772682244636110.1016/j.na.2007.08.042
H. G. Schuster. Reviews of Nonlinear Dynamics and Complexity1, Wiley-VCH Verlag Berlin GmbH, Weinheim, (2008).
DahalRGoodrichC SA uniformly sharp convexity result for discrete fractional sequential differencesRocky Mountain J. Math.201949825712586405833810.1216/RMJ-2019-49-8-2571
HendersonJNeugebauerJ TSmallest eigenvalues for a fractional difference equation with right focal boundary conditionsJ. Difference Equ. Appl.201723813171323370298110.1080/10236198.2017.1321641
PodlubnyIFractional Differential Equations1999San Diego, CAAcademic Press, Inc0924.34008
DiethelmKFordN JFreedA DLuchkoY FAlgorithms for the fractional calculus: a selection of numerical methodsComput. Methods Appl. Mech. Engrg.20051946-8743773210564810.1016/j.cma.2004.06.006
HendersonJExistence of local solutions for fractional difference equations with Dirichlet boundary conditionsJ. Difference Equ. Appl.2019256751756399100410.1080/10236198.2018.1505882
ChenCBohnerMJiaBUlam–Hyers stability of Caputo fractional difference equationsMath. Methods Appl. Sci.2019421874617470403798310.1002/mma.5869
IslamM NNeugebauerJ TInitial value problems for fractional differential equations of Riemann-Liouville typeAdv. Dyn. Syst. Appl.202015211312441530811454.34017
HolmMSum and difference compositions in discrete fractional calculusCubo2011133153184289548210.4067/S0719-06462011000300009
JonnalagaddaJ MDiscrete fractional Lyapunov-type inequalities in nabla senseDyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal202027639741941332561454.39019
DiethelmKFordN JAnalysis of fractional differential equationsJ. Math. Anal. Appl.20022652229248187613710.1006/jmaa.2000.7194
GoodrichC SPetersonA CDiscrete Fractional Calculus2015ChamSpringer10.1007/978-3-319-25562-0
AgarwalR PMeehanMO’ReganDFixed Point Theory and Applications2001CambridgeCambridge University Press10.1017/CBO9780511543005
ChatzarakisG ESelvamG MJanagarajRMiliarasG NOscillation criteria for a class of nonlinear discrete fractional order equations with damping termMath. Slovaca202070511651182415681610.1515/ms-2017-0422
GoodrichC SExistence of a positive solution to a system of discrete fractional boundary value problemsAppl. Math. Comput.201121794740475327451531215.39003
ChenCMertRJiaBErbeLPetersonAGronwall’s inequality for a nabla fractional difference system with a retarded argument and an applicationJ. Difference Equ. Appl.2019256855868399101110.1080/10236198.2019.1581180
AtιcιF MŠengülSModeling with fractional difference equationsJ. Math. Anal. Appl.2010369119264383910.1016/j.jmaa.2010.02.009
EloeP WKublikC MNeugebauerJ TComparison of Green’s functions for a family of boundary value problems for fractional difference equationsJ. Difference Equ. Appl.2019256776787399100610.1080/10236198.2018.1531129
M Bohner (24061777_CR5) 2018; 32
A Cabada (24061777_CR6) 2020; 23
C S Goodrich (24061777_CR22) 2021; 20
J Henderson (24061777_CR25) 2019; 25
C S Goodrich (24061777_CR20) 2011; 217
N Fewster-Young (24061777_CR17) 2012; 75
J Henderson (24061777_CR26) 2017; 23
G E Chatzarakis (24061777_CR7) 2020; 70
M Holm (24061777_CR27) 2011; 13
24061777_CR36
C Chen (24061777_CR8) 2019; 22
V Lakshmikantham (24061777_CR32) 2008; 69
K Diethelm (24061777_CR14) 2002; 265
A A Kilbas (24061777_CR30) 2006
K Diethelm (24061777_CR13) 2010
D B Pachpatte (24061777_CR33) 2020; 8
C S Goodrich (24061777_CR19) 2010; 5
C S Goodrich (24061777_CR21) 2011; 3
M N Islam (24061777_CR28) 2020; 15
P Hartman (24061777_CR24) 1960; 96
F M Atιcι (24061777_CR3) 2011; 17
F M Atιcι (24061777_CR2) 2010; 369
C Chen (24061777_CR11) 2019; 25
A Pratap (24061777_CR35) 2021; 44
R P Agarwal (24061777_CR1) 2001
C Chen (24061777_CR10) 2020; 44
F M Atιcι (24061777_CR4) 2012; 64
K Diethelm (24061777_CR15) 2005; 194
A G M Selvam (24061777_CR37) 2020; 2020
C Chen (24061777_CR9) 2019; 42
P W Eloe (24061777_CR16) 2019; 25
C S Goodrich (24061777_CR23) 2015
R Dahal (24061777_CR12) 2019; 49
I Podlubny (24061777_CR34) 1999
M Garić-Demirović (24061777_CR18) 2020; 2020
J M Jonnalagadda (24061777_CR29) 2020; 27
V Lakshmikantham (24061777_CR31) 2007; 11
References_xml – reference: GoodrichC SExistence of a positive solution to a system of discrete fractional boundary value problemsAppl. Math. Comput.201121794740475327451531215.39003
– reference: LakshmikanthamVVatsalaA SBasic theory of fractional differential equationsNonlinear Anal.200869826772682244636110.1016/j.na.2007.08.042
– reference: GoodrichC SSome new existence results for fractional difference equationsInt. J. Dyn. Syst. Differ. Equ.201131-214516227970461215.39004
– reference: DiethelmKFordN JAnalysis of fractional differential equationsJ. Math. Anal. Appl.20022652229248187613710.1006/jmaa.2000.7194
– reference: PachpatteD BBagwanA SKhandagaleA DExistence of solutions to discrete boundary value problem of fractional difference equationsMalaya J. Mat.202083832837411260810.26637/MJM0803/0017
– reference: ChatzarakisG ESelvamG MJanagarajRMiliarasG NOscillation criteria for a class of nonlinear discrete fractional order equations with damping termMath. Slovaca202070511651182415681610.1515/ms-2017-0422
– reference: ChenCBohnerMJiaBExistence and uniqueness of solutions for nonlinear Caputo fractional difference equationsTurkish J. Math.2020443857869410048310.3906/mat-1904-29
– reference: CabadaADimitrovNNontrivial solutions of non-autonomous Dirichlet fractional discrete problemsFract. Calc. Appl. Anal.2020234980995415109410.1515/fca-2020-0051
– reference: IslamM NNeugebauerJ TInitial value problems for fractional differential equations of Riemann-Liouville typeAdv. Dyn. Syst. Appl.202015211312441530811454.34017
– reference: AtιcιF MEloeP WGronwall’s inequality on discrete fractional calculusComput. Math. Appl.2012641031933200298934710.1016/j.camwa.2011.11.029
– reference: KilbasA ASrivastavaH MTrujilloJ JTheory and Applications of Fractional Differential Equations2006AmsterdamElsevier Science B.V1092.45003
– reference: AgarwalR PMeehanMO’ReganDFixed Point Theory and Applications2001CambridgeCambridge University Press10.1017/CBO9780511543005
– reference: HendersonJNeugebauerJ TSmallest eigenvalues for a fractional difference equation with right focal boundary conditionsJ. Difference Equ. Appl.201723813171323370298110.1080/10236198.2017.1321641
– reference: Fewster-YoungNTisdellC CThe existence of solutions to second-order singular boundary value problemsNonlinear Anal.2012751347984806292754510.1016/j.na.2012.03.029
– reference: GoodrichC SLyonsBVelcsovM TAnalytical and numerical monotonicity results for discrete fractional sequential differences with negative lower boundCommun. Pure Appl. Anal.2021201339358419150810.3934/cpaa.2020269
– reference: DahalRGoodrichC SA uniformly sharp convexity result for discrete fractional sequential differencesRocky Mountain J. Math.201949825712586405833810.1216/RMJ-2019-49-8-2571
– reference: DiethelmKThe Analysis of Fractional Differential Equations2010WarsawVersita10.1007/978-3-642-14574-2
– reference: HendersonJExistence of local solutions for fractional difference equations with Dirichlet boundary conditionsJ. Difference Equ. Appl.2019256751756399100410.1080/10236198.2018.1505882
– reference: ChenCBohnerMJiaBMethod of upper and lower solutions for nonlinear Caputo fractional difference equations and its applicationsFract. Calc. Appl. Anal.201922513071320404457610.1515/fca-2019-0069
– reference: Garić-DemirovićMMoranjkićSNurkanovićMNurkanovićZStability, Neimark–Sacker bifurcation, and approximation of the invariant curve of certain homogeneous second-order fractional difference equationDiscrete Dyn. Nat. Soc.2020202012413533410.1155/2020/6254013
– reference: BohnerMStamovaI MAn impulsive delay discrete stochastic neural network fractional-order model and applications in financeFilomat2018321863396352389942210.2298/FIL1818339B
– reference: HartmanPOn boundary value problems for systems of ordinary, nonlinear, second order differential equationsTrans. Amer. Math. Soc.19609649350912455310.1090/S0002-9947-1960-0124553-5
– reference: EloeP WKublikC MNeugebauerJ TComparison of Green’s functions for a family of boundary value problems for fractional difference equationsJ. Difference Equ. Appl.2019256776787399100610.1080/10236198.2018.1531129
– reference: LakshmikanthamVVatsalaA STheory of fractional differential inequalities and applicationsCommun. Appl. Anal.2007113-439540223681911159.34006
– reference: PratapARajaRCaoJHuangCNiezabitowskiMBagdasarOStability of discrete-time fractional-order time-delayed neural networks in complex fieldMath. Methods Appl. Sci.2021441419440418526210.1002/mma.6745
– reference: ChenCMertRJiaBErbeLPetersonAGronwall’s inequality for a nabla fractional difference system with a retarded argument and an applicationJ. Difference Equ. Appl.2019256855868399101110.1080/10236198.2019.1581180
– reference: GoodrichC SPetersonA CDiscrete Fractional Calculus2015ChamSpringer10.1007/978-3-319-25562-0
– reference: PodlubnyIFractional Differential Equations1999San Diego, CAAcademic Press, Inc0924.34008
– reference: DiethelmKFordN JFreedA DLuchkoY FAlgorithms for the fractional calculus: a selection of numerical methodsComput. Methods Appl. Mech. Engrg.20051946-8743773210564810.1016/j.cma.2004.06.006
– reference: AtιcιF MEloeP WTwo-point boundary value problems for finite fractional difference equationsJ. Difference Equ. Appl.2011174445456278335910.1080/10236190903029241
– reference: AtιcιF MŠengülSModeling with fractional difference equationsJ. Math. Anal. Appl.2010369119264383910.1016/j.jmaa.2010.02.009
– reference: HolmMSum and difference compositions in discrete fractional calculusCubo2011133153184289548210.4067/S0719-06462011000300009
– reference: SelvamA G MAlzabutJDhineshbabuRRashidSRehmanMDiscrete fractional order two-point boundary value problem with some relevant physical applicationsJ. Inequal. Appl.2020202019415289810.1186/s13660-020-02485-8
– reference: JonnalagaddaJ MDiscrete fractional Lyapunov-type inequalities in nabla senseDyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal202027639741941332561454.39019
– reference: GoodrichC SSolutions to a discrete right-focal fractional boundary value problemInt. J. Difference Equ.2010521952162771325
– reference: ChenCBohnerMJiaBUlam–Hyers stability of Caputo fractional difference equationsMath. Methods Appl. Sci.2019421874617470403798310.1002/mma.5869
– reference: H. G. Schuster. Reviews of Nonlinear Dynamics and Complexity1, Wiley-VCH Verlag Berlin GmbH, Weinheim, (2008).
– volume: 11
  start-page: 395
  issue: 3-4
  year: 2007
  ident: 24061777_CR31
  publication-title: Commun. Appl. Anal.
– volume: 369
  start-page: 1
  issue: 1
  year: 2010
  ident: 24061777_CR2
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2010.02.009
– volume: 96
  start-page: 493
  year: 1960
  ident: 24061777_CR24
  publication-title: Trans. Amer. Math. Soc.
  doi: 10.1090/S0002-9947-1960-0124553-5
– volume: 22
  start-page: 1307
  issue: 5
  year: 2019
  ident: 24061777_CR8
  publication-title: Fract. Calc. Appl. Anal.
  doi: 10.1515/fca-2019-0069
– volume: 194
  start-page: 743
  issue: 6-8
  year: 2005
  ident: 24061777_CR15
  publication-title: Comput. Methods Appl. Mech. Engrg.
  doi: 10.1016/j.cma.2004.06.006
– ident: 24061777_CR36
  doi: 10.1002/9783527626359
– volume: 44
  start-page: 857
  issue: 3
  year: 2020
  ident: 24061777_CR10
  publication-title: Turkish J. Math.
  doi: 10.3906/mat-1904-29
– volume: 2020
  start-page: 12
  year: 2020
  ident: 24061777_CR18
  publication-title: Discrete Dyn. Nat. Soc.
  doi: 10.1155/2020/6254013
– volume: 5
  start-page: 195
  issue: 2
  year: 2010
  ident: 24061777_CR19
  publication-title: Int. J. Difference Equ.
– volume-title: The Analysis of Fractional Differential Equations
  year: 2010
  ident: 24061777_CR13
  doi: 10.1007/978-3-642-14574-2
– volume-title: Theory and Applications of Fractional Differential Equations
  year: 2006
  ident: 24061777_CR30
– volume: 70
  start-page: 1165
  issue: 5
  year: 2020
  ident: 24061777_CR7
  publication-title: Math. Slovaca
  doi: 10.1515/ms-2017-0422
– volume: 64
  start-page: 3193
  issue: 10
  year: 2012
  ident: 24061777_CR4
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2011.11.029
– volume: 3
  start-page: 145
  issue: 1-2
  year: 2011
  ident: 24061777_CR21
  publication-title: Int. J. Dyn. Syst. Differ. Equ.
– volume: 8
  start-page: 832
  issue: 3
  year: 2020
  ident: 24061777_CR33
  publication-title: Malaya J. Mat.
  doi: 10.26637/MJM0803/0017
– volume: 32
  start-page: 6339
  issue: 18
  year: 2018
  ident: 24061777_CR5
  publication-title: Filomat
  doi: 10.2298/FIL1818339B
– volume: 42
  start-page: 7461
  issue: 18
  year: 2019
  ident: 24061777_CR9
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.5869
– volume: 25
  start-page: 855
  issue: 6
  year: 2019
  ident: 24061777_CR11
  publication-title: J. Difference Equ. Appl.
  doi: 10.1080/10236198.2019.1581180
– volume: 13
  start-page: 153
  issue: 3
  year: 2011
  ident: 24061777_CR27
  publication-title: Cubo
  doi: 10.4067/S0719-06462011000300009
– volume: 20
  start-page: 339
  issue: 1
  year: 2021
  ident: 24061777_CR22
  publication-title: Commun. Pure Appl. Anal.
  doi: 10.3934/cpaa.2020269
– volume-title: Fixed Point Theory and Applications
  year: 2001
  ident: 24061777_CR1
  doi: 10.1017/CBO9780511543005
– volume-title: Fractional Differential Equations
  year: 1999
  ident: 24061777_CR34
– volume: 2020
  start-page: 19
  year: 2020
  ident: 24061777_CR37
  publication-title: J. Inequal. Appl.
  doi: 10.1186/s13660-020-02485-8
– volume: 265
  start-page: 229
  issue: 2
  year: 2002
  ident: 24061777_CR14
  publication-title: J. Math. Anal. Appl.
  doi: 10.1006/jmaa.2000.7194
– volume: 25
  start-page: 776
  issue: 6
  year: 2019
  ident: 24061777_CR16
  publication-title: J. Difference Equ. Appl.
  doi: 10.1080/10236198.2018.1531129
– volume: 25
  start-page: 751
  issue: 6
  year: 2019
  ident: 24061777_CR25
  publication-title: J. Difference Equ. Appl.
  doi: 10.1080/10236198.2018.1505882
– volume: 69
  start-page: 2677
  issue: 8
  year: 2008
  ident: 24061777_CR32
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2007.08.042
– volume: 23
  start-page: 980
  issue: 4
  year: 2020
  ident: 24061777_CR6
  publication-title: Fract. Calc. Appl. Anal.
  doi: 10.1515/fca-2020-0051
– volume: 23
  start-page: 1317
  issue: 8
  year: 2017
  ident: 24061777_CR26
  publication-title: J. Difference Equ. Appl.
  doi: 10.1080/10236198.2017.1321641
– volume: 15
  start-page: 113
  issue: 2
  year: 2020
  ident: 24061777_CR28
  publication-title: Adv. Dyn. Syst. Appl.
– volume: 17
  start-page: 445
  issue: 4
  year: 2011
  ident: 24061777_CR3
  publication-title: J. Difference Equ. Appl.
  doi: 10.1080/10236190903029241
– volume: 44
  start-page: 419
  issue: 1
  year: 2021
  ident: 24061777_CR35
  publication-title: Math. Methods Appl. Sci.
  doi: 10.1002/mma.6745
– volume: 27
  start-page: 397
  issue: 6
  year: 2020
  ident: 24061777_CR29
  publication-title: Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal
– volume: 75
  start-page: 4798
  issue: 13
  year: 2012
  ident: 24061777_CR17
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2012.03.029
– volume: 217
  start-page: 4740
  issue: 9
  year: 2011
  ident: 24061777_CR20
  publication-title: Appl. Math. Comput.
– volume-title: Discrete Fractional Calculus
  year: 2015
  ident: 24061777_CR23
  doi: 10.1007/978-3-319-25562-0
– volume: 49
  start-page: 2571
  issue: 8
  year: 2019
  ident: 24061777_CR12
  publication-title: Rocky Mountain J. Math.
  doi: 10.1216/RMJ-2019-49-8-2571
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Snippet In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence...
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SubjectTerms 39A12
39A27
39A70
Abstract Harmonic Analysis
Analysis
boundary value problem
Boundary value problems
discrete fractional calculus
discrete fractional inequalities
existence of solutions
Existence theorems
Fixed points (mathematics)
Functional Analysis
Inequalities
Integral Transforms
Mathematics
Operational Calculus
Primary 26A33
Research Paper
Secondary 34A08
Title Discrete Fractional Boundary Value Problems and Inequalities
URI https://link.springer.com/article/10.1515/fca-2021-0077
https://www.degruyter.com/doi/10.1515/fca-2021-0077
https://www.proquest.com/docview/2601249580
Volume 24
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