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Volumn 2010, Issue , 2010, Pages 1-16

Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions

Author keywords

Boundary value problem; Caputo fractional derivative; Differential inclusion; Existence; Fixed point; Fractional integral; Integral conditions; Uniqueness

Indexed keywords


EID: 77955452631     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (59)

References (53)
  • 1
    • 46549103408 scopus 로고
    • Cellular systems and aging models
    • G. Adomian and G. E. Adomian, Cellular systems and aging models, Comput. Math. Appl. 11 (1985) 283-291.
    • (1985) Comput. Math. Appl , vol.11 , pp. 283-291
    • Adomian, G.1    Adomian, G.E.2
  • 2
    • 42649131330 scopus 로고    scopus 로고
    • Boundary value problems for fractional differential equations
    • R. P. Agarwal, M. Benchohra, and S. Hamani, Boundary value problems for fractional differential equations, Adv. Stud. Contemp. Math. 16 (2) (2008), 181-196.
    • (2008) Adv. Stud. Contemp. Math , vol.16 , Issue.2 , pp. 181-196
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 5
    • 77949268160 scopus 로고    scopus 로고
    • Existence theory for perturbed boundary value problems with integral boundary conditions
    • A. Belarbi, M. Benchohra, and B. C. Dhage, Existence theory for perturbed boundary value problems with integral boundary conditions, Georgian Math. J., 13 (2) (2006), 215-228.
    • (2006) Georgian Math. J , vol.13 , Issue.2 , pp. 215-228
    • Belarbi, A.1    Benchohra, M.2    Dhage, B.C.3
  • 6
    • 37349041073 scopus 로고    scopus 로고
    • Perturbed functional differential equations with fractional order, Commun
    • A. Belarbi, M. Benchohra, S. Hamani, and S. K. Ntouyas, Perturbed functional differential equations with fractional order, Commun. Appl. Anal. 11 (3-4) (2007), 429-440.
    • (2007) Appl. Anal , vol.11 , Issue.3-4 , pp. 429-440
    • Belarbi, A.1    Benchohra, M.2    Hamani, S.3    Ntouyas, S.K.4
  • 7
    • 38149134242 scopus 로고    scopus 로고
    • Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces
    • A. Belarbi, M. Benchohra and A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal. 85 (2006), 1459-1470.
    • (2006) Appl. Anal , vol.85 , pp. 1459-1470
    • Belarbi, A.1    Benchohra, M.2    Ouahab, A.3
  • 8
    • 58249117112 scopus 로고    scopus 로고
    • Existence results for boundary value problems with nonlinear fractional differential equations
    • M. Benchohra, J. R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008), 851-863.
    • (2008) Appl. Anal , vol.87 , pp. 851-863
    • Benchohra, M.1    Graef, J.R.2    Hamani, S.3
  • 9
    • 70350087351 scopus 로고    scopus 로고
    • Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative
    • M. Benchohra and S. Hamani, Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative, Topol. Meth. Nonlinear Anal., 32 (1) (2008), 115-130.
    • (2008) Topol. Meth. Nonlinear Anal , vol.32 , Issue.1 , pp. 115-130
    • Benchohra, M.1    Hamani, S.2
  • 11
    • 67651193694 scopus 로고    scopus 로고
    • The method of upper and lower solutions for second order differential inclusions with integral boundary conditions
    • (to appear)
    • M. Benchohra, S. Hamani, and J. J. Nieto, The method of upper and lower solutions for second order differential inclusions with integral boundary conditions, Rocky Mountain J. Math. (to appear).
    • Rocky Mountain J. Math
    • Benchohra, M.1    Hamani, S.2    Nieto, J.J.3
  • 12
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2) (2008), 1340-1350.
    • (2008) J. Math. Anal. Appl , vol.338 , Issue.2 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 13
    • 77949273090 scopus 로고    scopus 로고
    • Analysis of age structured host-parasitoid model, Far East
    • K. W. Blayneh, Analysis of age structured host-parasitoid model, Far East J. Dyn. Syst. 4 (2002), 125-145.
    • (2002) J. Dyn. Syst , vol.4 , pp. 125-145
    • Blayneh, K.W.1
  • 14
    • 0002110530 scopus 로고
    • Extensions and selections of maps with decomposable values
    • A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
    • (1988) Studia Math , vol.90 , pp. 69-86
    • Bressan, A.1    Colombo, G.2
  • 15
    • 0003211244 scopus 로고
    • Convex Analysis and Measurable Multifunctions
    • Springer-Verlag, Berlin-Heidelberg-New York
    • C. Castaing and 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
  • 16
    • 51249191814 scopus 로고
    • Multivalued contraction mappings in generalized metric spaces
    • H. Covitz and S. B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
    • (1970) Israel J. Math , vol.8 , pp. 5-11
    • Covitz, H.1    Nadler Jr, S.B.2
  • 17
    • 33845961350 scopus 로고    scopus 로고
    • Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives
    • V. Daftardar-Gejji and H. Jafari, Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives. J. Math. Anal. Appl. 328 (2) (2007), 1026-1033.
    • (2007) J. Math. Anal. Appl , vol.328 , Issue.2 , pp. 1026-1033
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 19
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • D. Delbosco and 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
  • 21
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002), 229-248.
    • (2002) J. Math. Anal. Appl , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 22
    • 0043044718 scopus 로고    scopus 로고
    • Numerical solution of fractional order differential equations by extrapolation
    • K. Diethelm and G. Walz, Numerical solution of fractional order differential equations by extrapolation, Numer. Algorithms 16 (1997), 231-253.
    • (1997) Numer. Algorithms , vol.16 , pp. 231-253
    • Diethelm, K.1    Walz, G.2
  • 23
    • 0038086852 scopus 로고
    • Fractional order evolution equations
    • A. M. A. El-Sayed, Fractional order evolution equations, J. Fract. Calc. 7 (1995), 89-100.
    • (1995) J. Fract. Calc , vol.7 , pp. 89-100
    • El-Sayed, A.M.A.1
  • 24
    • 0030531939 scopus 로고    scopus 로고
    • Fractional order diffusion-wave equations
    • A. M. A. El-Sayed, Fractional order diffusion-wave equations, Intern. J. Theo. Physics 35 (1996), 311-322.
    • (1996) Intern. J. Theo. Physics , vol.35 , pp. 311-322
    • El-Sayed, A.M.A.1
  • 25
    • 0032115069 scopus 로고    scopus 로고
    • Nonlinear functional differential equations of arbitrary orders
    • A. M. A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998), 181-186.
    • (1998) Nonlinear Anal , vol.33 , pp. 181-186
    • El-Sayed, A.M.A.1
  • 26
    • 0011605117 scopus 로고
    • Théorèmes d'existence pour des inclusions différentielles sans convexité
    • M. Frigon and A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité, C. R. Acad. Sci. Paris, Ser. I 310 (1990), 819-822.
    • (1990) C. R. Acad. Sci. Paris, Ser. I , vol.310 , pp. 819-822
    • Frigon, M.1    Granas, A.2
  • 28
    • 21344459444 scopus 로고    scopus 로고
    • An existence result for a nonlocal fractional differential problem
    • K. M. Furati and N-e. Tatar, An existence result for a nonlocal fractional differential problem. J. Fract. Calc. 26 (2004), 43-51.
    • (2004) J. Fract. Calc , vol.26 , pp. 43-51
    • Furati, K.M.1    Tatar, N-e.2
  • 29
    • 34147133470 scopus 로고    scopus 로고
    • Behavior of solutions for a weighted Cauchy-type fractional differential problem
    • K. M. Furati and N-e. Tatar, Behavior of solutions for a weighted Cauchy-type fractional differential problem. J. Fract. Calc. 28 (2005), 23-42.
    • (2005) J. Fract. Calc , vol.28 , pp. 23-42
    • Furati, K.M.1    Tatar, N-e.2
  • 30
    • 44949282247 scopus 로고
    • Damping description involving fractional operators, Mech
    • L. Gaul, P. Klein, and S. Kempfle, Damping description involving fractional operators, Mech. Systems Signal Processing 5 (1991), 81-88.
    • (1991) Systems Signal Processing , vol.5 , pp. 81-88
    • Gaul, L.1    Klein, P.2    Kempfle, S.3
  • 31
    • 0028878140 scopus 로고
    • A fractional calculus approach of self-similar protein dynamics
    • W. G. Glockle and T. F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68 (1995), 46-53.
    • (1995) Biophys. J , vol.68 , pp. 46-53
    • Glockle, W.G.1    Nonnenmacher, T.F.2
  • 33
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • N. Heymans and I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 45 (5) (2006), 765-772.
    • (2006) Rheologica Acta , vol.45 , Issue.5 , pp. 765-772
    • Heymans, N.1    Podlubny, I.2
  • 36
    • 58249115464 scopus 로고    scopus 로고
    • Positive solutions of a boundary value problem for a nonlinear fractional differential equation
    • E. R. Kaufmann and E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 2007, No. 3, 11 pp.
    • (2007) Electron. J. Qual. Theory Differ. Equ , vol.3 , pp. 11
    • Kaufmann, E.R.1    Mboumi, E.2
  • 37
    • 17444382726 scopus 로고    scopus 로고
    • Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
    • A. A. Kilbas and S. A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differential Equations 41 (2005), 84-89.
    • (2005) Differential Equations , vol.41 , pp. 84-89
    • Kilbas, A.A.1    Marzan, S.A.2
  • 38
    • 77956684069 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • Elsevier Science B.V., Amsterdam
    • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
    • (2006) North-Holland Mathematics Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 40
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • (A. Carpinteri and F. Mainardi, Eds), Springer-Verlag, Wien
    • F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in "Fractals and Fractional Calculus in Continuum Mechanics" (A. Carpinteri and F. Mainardi, Eds), pp. 291-348, Springer-Verlag, Wien, 1997.
    • (1997) Fractals and Fractional Calculus In Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 41
    • 0001044887 scopus 로고
    • Relaxation in filled polymers: A fractional calculus approach
    • F. Metzler, W. Schick, H. G. Kilian, and 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, F.1    Schick, W.2    Kilian, H.G.3    Nonnenmacher, T.F.4
  • 43
    • 34848921672 scopus 로고    scopus 로고
    • Some comparison results for integro-fractional differential inequalities
    • S. M. Momani and S. B. Hadid, Some comparison results for integro-fractional differential inequalities. J. Fract. Calc. 24 (2003), 37-44.
    • (2003) J. Fract. Calc , vol.24 , pp. 37-44
    • Momani, S.M.1    Hadid, S.B.2
  • 44
    • 17844385541 scopus 로고    scopus 로고
    • Some analytical properties of solutions of differential equations of noninteger order
    • S. M. Momani, S. B. Hadid, and Z. M. Alawenh, Some analytical properties of solutions of differential equations of noninteger order, Int. J. Math. Math. Sci. 2004 (2004), 697-701.
    • (2004) Int. J. Math. Math. Sci , vol.2004 , pp. 697-701
    • Momani, S.M.1    Hadid, S.B.2    Alawenh, Z.M.3
  • 45
    • 77955453578 scopus 로고
    • The Fractional Calculus, Academic Press, New York
    • K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974.
    • (1974) London
    • Oldham, K.B.1    Spanier, J.2
  • 46
    • 53949105887 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 (2008), 3877-3896.
    • (2008) Nonlinear Anal , vol.69 , pp. 3877-3896
    • Ouahab, A.1
  • 48
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calculus Appl. Anal. 5 (2002), 367-386.
    • (2002) Fract. Calculus Appl. Anal , vol.5 , pp. 367-386
    • Podlubny, I.1
  • 51
    • 0004021335 scopus 로고
    • 6th edn. Springer-Verlag, Berlin
    • K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin, 1980.
    • (1980) Functional Analysis
    • Yosida, K.1
  • 52
    • 23844442815 scopus 로고    scopus 로고
    • Existence of fractional differential equations
    • C. Yu and G. Gao, Existence of fractional differential equations, J. Math. Anal. Appl. 310 (2005), 26-29.
    • (2005) J. Math. Anal. Appl , vol.310 , pp. 26-29
    • Yu, C.1    Gao, G.2
  • 53
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional differential equations
    • S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Diff. Equ. 2006, No. 36, pp. 1-12.
    • (2006) Electron. J. Diff. Equ , vol.36 , pp. 1-12
    • Zhang, S.1


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