메뉴 건너뛰기




Volumn 2012, Issue , 2012, Pages

Existence of multiple positive solutions for fractional differential inclusions with m-point boundary conditions and two fractional orders

Author keywords

Cone; Fixed point theorem; Fractional derivative; Inclusion; Multi point boundary value problem

Indexed keywords


EID: 84868608487     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (45)
  • 1
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • R. P. Agarwal, M. Benchohra, S. Hamani; A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109, 973-1033 (2010).
    • (2010) Acta Appl. Math , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 3
    • 0038405057 scopus 로고    scopus 로고
    • Existence of positive solutions of nonlinear fractional Differential equations
    • A. Babakhani, V. D. Gejji; Existence of positive solutions of nonlinear fractional Differential equations, J. math. Anal. Appl. 278 (2003) 434-442.
    • (2003) J. Math. Anal. Appl , vol.278 , pp. 434-442
    • Babakhani, A.1    Gejji, V.D.2
  • 4
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Z. B. Bai, H. S. Lü; Positive solutions for boundary value problem of nonlinear fractional differential equation, J. math. Anal. Appl. 311 (2005) 495-505.
    • (2005) J. Math. Anal. Appl , vol.311 , pp. 495-505
    • Bai, Z.B.1    Lü, H.S.2
  • 5
    • 58149196822 scopus 로고    scopus 로고
    • Existence results for fractional or- der functional differential inclusions with infinite delay and applications to control theory
    • M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab; Existence results for fractional or- der functional differential inclusions with infinite delay and applications to control theory, Fract. Calc. Appl. Anal. 11 (2008), 35-56.
    • (2008) Fract. Calc. Appl. Anal , vol.11 , pp. 35-56
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 7
    • 0002110530 scopus 로고
    • Extensions and selections of maps with decomposable values
    • A. Bressan, G. Colombo; Extensions and selections of maps with decomposable values, Studia Math. 90 (1988) 70-85.
    • (1988) Studia Math , vol.90 , pp. 70-85
    • Bressan, A.1    Colombo, G.2
  • 8
    • 0003211244 scopus 로고
    • Convex Analysis and Measurable Multifunctions
    • Springer-Verlag, Berlin-Heidelberg-New York
    • C. Castaing, M. Valadier; Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
    • (1977) Lecture Notes In Mathematics , vol.580
    • Castaing, C.1    Valadier, M.2
  • 9
    • 71749083785 scopus 로고    scopus 로고
    • Continuous version of Filippovs theorem for fractional differential inclusions
    • A. Cernea; Continuous version of Filippovs theorem for fractional differential inclusions, Nonlinear Anal. 72 (2010), 204-208.
    • (2010) Nonlinear Anal , vol.72 , pp. 204-208
    • Cernea, A.1
  • 10
    • 77958085118 scopus 로고    scopus 로고
    • Antiperiodic solutions for Lienard-type differential equation with p-Laplacian operator
    • Article ID 194824
    • T. Chen, W. Liu, C. Yang; Antiperiodic solutions for Lienard-type differential equation with p-Laplacian operator, Bound.Value Probl. 2010 (2010) 1-12. Article ID 194824.
    • (2010) Bound.Value Probl , vol.2010 , pp. 1-12
    • Chen, T.1    Liu, W.2    Yang, C.3
  • 11
    • 51249191814 scopus 로고
    • Multivalued contraction mappings in generalized metric spaces, Israel
    • H. Covitz, S. B. Nadler Jr.; Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970) 5-11.
    • (1970) J. Math , vol.8 , pp. 5-11
    • Covitz, H.1    Nadler Jr., S.B.2
  • 13
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional Differential equation
    • D. Delbosco, L. Rodino; Existence and uniqueness for a nonlinear fractional Differential equation, J. math. Anal. Appl. 204 (1996) 609-625.
    • (1996) J. Math. Anal. Appl , vol.204 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 15
    • 4043121080 scopus 로고    scopus 로고
    • Detailed error analysis for a fractional Adams Method
    • K. Diethelml, N. Ford, A. Freed, Detailed error analysis for a fractional Adams Method. Numer. Algorithms 36, 31-52 (2004).
    • (2004) Numer. Algorithms , vol.36 , pp. 31-52
    • Diethelml, K.1    Ford, N.2    Freed, A.3
  • 16
    • 0011605117 scopus 로고
    • Théorèmes d'existence pour les inclusions différentiwlles sans convexité
    • M. Frignon, A. Granas; Théorèmes d'existence pour les inclusions différentiwlles sans convexité, C. R. Acad. Sci. Paris I 310 (1990) 819-822.
    • (1990) C. R. Acad. Sci. Paris , vol.1 , Issue.310 , pp. 819-822
    • Frignon, M.1    Granas, A.2
  • 17
    • 44949282247 scopus 로고
    • Damping description involving fractional operators
    • L. Gaul, P. Klein, S. Kemple; Damping description involving fractional operators, Mech. Syst. Signal Process 5 (1991) 81-88.
    • (1991) Mech. Syst. Signal Process , vol.5 , pp. 81-88
    • Gaul, L.1    Klein, P.2    Kemple, S.3
  • 18
    • 0028878140 scopus 로고
    • A fractional calculus approach to self-semilar protein dynamics
    • W. G. Glockle, T. F. Nonnenmacher; A fractional calculus approach to self-semilar protein dynamics, Biophys. J. 68 (1995) 46-53.
    • (1995) Biophys. J , vol.68 , pp. 46-53
    • Glockle, W.G.1    Nonnenmacher, T.F.2
  • 20
    • 58149326839 scopus 로고    scopus 로고
    • On the fractional order m-point boundary value problem in reflexive Banach spaces and Weak topologies
    • Hussein. A. H. Salem; On the fractional order m-point boundary value problem in reflexive Banach spaces and Weak topologies, J. Comput. Appl. Math. 224(2009) 565-572.
    • (2009) J. Comput. Appl. Math , vol.224 , pp. 565-572
    • Salem, H.A.H.1
  • 21
    • 0011639086 scopus 로고
    • Multivalued fractional differential equations of arbitrary orders, Springer-Verlag
    • A.M.A. El-Sayed, A.G. Ibrahim; Multivalued fractional differential equations of arbitrary orders, Springer-Verlag, Appl. Math. Comput. 68 (1995) 15-25.
    • (1995) Appl. Math. Comput , vol.68 , pp. 15-25
    • El-Sayed, A.M.A.1    Ibrahim, A.G.2
  • 22
    • 0034670596 scopus 로고    scopus 로고
    • Upper and lower solution method and a singular boundary value problem for the one-dimensional p-Laplacian
    • D. Jiang, W. Gao; Upper and lower solution method and a singular boundary value problem for the one-dimensional p-Laplacian, J. math. Anal. Appl. 252 (2000) 631-648.
    • (2000) J. Math. Anal. Appl , vol.252 , pp. 631-648
    • Jiang, D.1    Gao, W.2
  • 23
    • 0009953314 scopus 로고    scopus 로고
    • Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces
    • Walter de Gruyter, Berlin, New York
    • M. Kamenskii, V. Obukhovskii, P. Zecca; Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, in: Nonlin. Anal. Appl., vol. 7, Walter de Gruyter, Berlin, New York, 2001.
    • (2001) Nonlin. Anal. Appl , vol.7
    • Kamenskii, M.1    Obukhovskii, V.2    Zecca, P.3
  • 26
    • 53949111458 scopus 로고    scopus 로고
    • Basic theory of fractional differential equations
    • V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations. Nonlinear Anal. TMA 69 (8), 2677-2682 (2008).
    • (2008) Nonlinear Anal. TMA , vol.69 , Issue.8 , pp. 2677-2682
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 27
    • 0000394603 scopus 로고
    • Multiple positive fixed points of nonlinear operators on ordered Banach spaces
    • R. W. Leggett, L. R. Williams; Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J. 673-688(1979).
    • (1979) Indiana Univ. Math. J , pp. 673-688
    • Leggett, R.W.1    Williams, L.R.2
  • 28
    • 56249103610 scopus 로고    scopus 로고
    • The existence of solutions of m-point p-Laplacian boundary value problems at resonance
    • L. Lian, W. Ge; The existence of solutions of m-point p-Laplacian boundary value problems at resonance, Acta Math. Appl. Sin. 28 (2005) 288-295.
    • (2005) Acta Math. Appl. Sin , vol.28 , pp. 288-295
    • Lian, L.1    Ge, W.2
  • 29
    • 34548076507 scopus 로고    scopus 로고
    • On the existence of solutions for the periodic boundary value problems with p-Laplacian operator
    • B. Liu, J. Yu; On the existence of solutions for the periodic boundary value problems with p-Laplacian operator, J. Systems Sci. Math. Sci. 23 (2003) 76-85.
    • (2003) J. Systems Sci. Math. Sci , vol.23 , pp. 76-85
    • Liu, B.1    Yu, J.2
  • 30
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • Springer-Verlag, New York A.Carpinteri, Mainardi(Eds.)
    • F. Mainardi; Fractional calculus: some basic problems in continuum and statistical mechanics, in: A.Carpinteri, Mainardi(Eds.), Fractals and Fractional calculus in continuum mechanics, Springer-Verlag, New York, 1997.
    • Fractals and Fractional Calculus In Continuum Mechanics , pp. 1997
    • Mainardi, F.1
  • 31
    • 0001044887 scopus 로고
    • Relaxation in filled polymers: A fractional calculus approach
    • R. Metzler, W. Schick, H. G. Kilian, T. F. Nonnenmacher; Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys. 103 (1995) 7180-7186.
    • (1995) J. Chem. Phys , vol.103 , pp. 7180-7186
    • Metzler, R.1    Schick, W.2    Kilian, H.G.3    Nonnenmacher, T.F.4
  • 32
    • 84868603613 scopus 로고
    • Introduction to Functional Analysis, PWN
    • (in Polish)
    • J. Musielak; Introduction to Functional Analysis, PWN, Warsaw, 1976, (in Polish).
    • (1976) Warsaw
    • Musielak, J.1
  • 33
    • 84868604926 scopus 로고    scopus 로고
    • Existence of solutions for fractional differential inclusions with nonlocal strip conditions
    • B. Ahmad and S.K. Ntouyas; Existence of solutions for fractional differential inclusions with nonlocal strip conditions, Arab J. Math. Sci., 18 (2012), 121-134.
    • (2012) Arab J. Math. Sci , vol.18 , pp. 121-134
    • Ahmad, B.1    Ntouyas, S.K.2
  • 34
    • 84868609428 scopus 로고    scopus 로고
    • Existence of solutions for multi point boundary value problems for fractional differential equations
    • N. Nyamoradi; Existence of solutions for multi point boundary value problems for fractional differential equations, Arab J. Math. Sci., 18 (2012), 165-175.
    • (2012) Arab J. Math. Sci , vol.18 , pp. 165-175
    • Nyamoradi, N.1
  • 35
    • 84868603614 scopus 로고    scopus 로고
    • Positive Solutions for multi-point boundary value problem for nonlinear fractional differential equations
    • (Preprint)
    • N. Nyamoradi; Positive Solutions for multi-point boundary value problem for nonlinear fractional differential equations, J. Contemporary Math. Anal. (Preprint).
    • J. Contemporary Math. Anal
    • Nyamoradi, N.1
  • 36
    • 84870945253 scopus 로고    scopus 로고
    • A Six-point nonlocal integral boundary value problem for fractional differential equations
    • (Preprint)
    • N. Nyamoradi; A Six-point nonlocal integral boundary value problem for fractional differential equations, Indian J. Pure Appl. Math. (Preprint).
    • Indian J. Pure Appl. Math
    • Nyamoradi, N.1
  • 37
    • 84868607992 scopus 로고    scopus 로고
    • Multiple positive solutions for nonlinear fractional differential systems
    • N. Nyamoradi, T. Bashiri; Multiple positive solutions for nonlinear fractional differential systems, Fract. differen. calcul., 2 (2) (2012), 119-128.
    • (2012) Fract. Differen. Calcul , vol.2 , Issue.2 , pp. 119-128
    • Nyamoradi, N.1    Bashiri, T.2
  • 39
    • 42649111859 scopus 로고    scopus 로고
    • Some results for fractional boundary value problem of differential inclusions
    • A. Ouahab; Some results for fractional boundary value problem of differential inclusions, Nonlinear Anal. 69 (2009), 3871-3896.
    • (2009) Nonlinear Anal , vol.69 , pp. 3871-3896
    • Ouahab, A.1
  • 42
    • 0141508296 scopus 로고
    • Anomalous transit-time dispersion in amorphous solids
    • H. Scher, E. W. Montroll; Anomalous transit-time dispersion in amorphous solids, Phys. Rev. B 12 (1975) 2455-2477.
    • (1975) Phys. Rev. B , vol.12 , pp. 2455-2477
    • Scher, H.1    Montroll, E.W.2
  • 43
    • 1242327688 scopus 로고    scopus 로고
    • Differential equations of fractional order: Methods, results and problems I
    • A. A. Kilbas, J. J. Trujillo; Differential equations of fractional order: Methods, results and problems I, Appl. Anal. 78 (2001) 153-192.
    • (2001) Appl. Anal , vol.78 , pp. 153-192
    • Kilbas, A.A.1    Trujillo, J.J.2
  • 44
    • 25144514177 scopus 로고    scopus 로고
    • Differential equations of fractional order: Methods, results and problems II
    • A. A. Kilbas, J. J. Trujillo; Differential equations of fractional order: Methods, results and problems II, Appl. Anal. 81 (2002) 435-493.
    • (2002) Appl. Anal , vol.81 , pp. 435-493
    • Kilbas, A.A.1    Trujillo, J.J.2
  • 45
    • 56249133557 scopus 로고    scopus 로고
    • Multiple periodic solutions of p-Laplacian equation with one-side Nagumo condition
    • J. Zhang, W. Liu, J. Ni, T. Chen Multiple periodic solutions of p-Laplacian equation with one-side Nagumo condition, J. Korean. Math. Soc. 45 (2008) 1549-1559.
    • (2008) J. Korean. Math. Soc , vol.45 , pp. 1549-1559
    • Zhang, J.1    Liu, W.2    Ni, J.3    Chen, T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.