메뉴 건너뛰기




Volumn 55, Issue 3, 2009, Pages 221-230

On the application of measure of noncompactness to the existence of solutions for fractional differential equations

Author keywords

Banach space; Boundary value problem; Caputo fractional derivative; Fixed point; Measure of noncompactness

Indexed keywords


EID: 71149084117     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/s00025-009-0434-5     Document Type: Article
Times cited : (87)

References (37)
  • 1
    • 42649131330 scopus 로고    scopus 로고
    • Boundary value problems for differential inclusions with fractional order
    • R.P. Agarwal, M. Benchohra, S. Hamani, Boundary value problems for differential inclusions with fractional order. Adv. Stud. Contemp. Math. 12 (2) (2008), 181-196.
    • (2008) Adv. Stud. Contemp. Math. , vol.12 , Issue.2 , pp. 181-196
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 2
    • 71549167605 scopus 로고    scopus 로고
    • Boundary value problems for fractional differential equations
    • (to appear)
    • R.P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential equations. Georgian Math. J. (to appear).
    • Georgian Math. J.
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 6
    • 0011872091 scopus 로고
    • Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces
    • Madrid
    • J.C. Alàarez, Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces. Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid 79 (1985), 53-66.
    • (1985) Rev. Real. Acad. Cienc. Exact. Fis. Natur. , vol.79 , pp. 53-66
    • Alàarez, J.C.1
  • 7
    • 0042546240 scopus 로고    scopus 로고
    • Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the Lebesgue space
    • J. Banas̀, Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the Lebesgue space. Nonlinear Anal. 30 (1997), 3283-3293.
    • (1997) Nonlinear Anal. , vol.30 , pp. 3283-3293
    • Banas̀, J.1
  • 8
    • 45349090141 scopus 로고    scopus 로고
    • Global asymptotic stability of solutions of a fractional integral equation
    • J. Banas̀, B. C. Dhage, Global asymptotic stability of solutions of a fractional integral equation. Nonlinear Anal. 69 (2008), 1945-1952.
    • (2008) Nonlinear Anal. , vol.69 , pp. 1945-1952
    • Banas̀, J.1    Dhage, B.C.2
  • 9
  • 10
    • 1242313975 scopus 로고    scopus 로고
    • Measures of noncompactness related to monotonicity
    • J. Banas̀, L. Olszowy, Measures of noncompactness related to monotonicity. Comment. Math. 41 (2001), 13-23.
    • (2001) Comment. Math. , vol.41 , pp. 13-23
    • Banas̀, J.1    Olszowy, L.2
  • 11
    • 0037211696 scopus 로고    scopus 로고
    • An application of a measure of noncompactness in the study of asymptotique stability
    • J. Banas̀, B. Rzepka, An application of a measure of noncompactness in the study of asymptotique stability. Appl. Math. Lett. 16 (2003), 1-6.
    • (2003) Appl. Math. Lett. , vol.16 , pp. 1-6
    • Banas̀, J.1    Rzepka, B.2
  • 12
    • 35548975280 scopus 로고    scopus 로고
    • On some measures of noncompactness in the space of continuous functions
    • J. Banas̀, K. Sadarangani, On some measures of noncompactness in the space of continuous functions, Nonlinear Anal. 68 (2008), 377-383.
    • (2008) Nonlinear Anal. , vol.68 , pp. 377-383
    • Banas̀, J.1    Sadarangani, K.2
  • 13
    • 38149134242 scopus 로고    scopus 로고
    • Existance results for functional differential equations of fractional order
    • A. Belarbi, M. Benchohra, A. Ouahab, Existance results for functional differential equations of fractional order. Appl. Anal. 85 (2006), 1459-1470.
    • (2006) Appl. Anal. , vol.85 , pp. 1459-1470
    • Belarbi, A.1    Benchohra, M.2    Ouahab, A.3
  • 14
    • 58249103422 scopus 로고    scopus 로고
    • Boundary value problems for differential equations with fractional order
    • M. Benchohra, S. Hamani, S. K. Ntouyas, Boundary value problems for differential equations with fractional order. Surveys Math. Appl. 3 (2008), 1-12.
    • (2008) Surveys Math. Appl. , vol.3 , pp. 1-12
    • Benchohra, M.1    Hamani, S.2    Ntouyas, S.K.3
  • 15
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 332 (2) (2008), 1340-1350.
    • (2008) J. Math. Anal. Appl. , vol.332 , Issue.2 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 16
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • D. Delboso, 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
    • Delboso, D.1    Rodino, L.2
  • 17
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • K. Diethelm, 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
  • 20
    • 0028878140 scopus 로고
    • A fractional calculus approach of self-similar protein dynamics
    • W. G. Glockle, 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
  • 21
    • 0003658236 scopus 로고    scopus 로고
    • Nonlinear Integral Equations in Abstract Spaces
    • Kluwer Academic Publishers Group, Dordrecht
    • D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces. Mathematics and its Applications, 373. Kluwer Academic Publishers Group, Dordrecht, 1996
    • (1996) Mathematics and its Applications , vol.373
    • Guo, D.1    Lakshmikantham, V.2    Liu, X.3
  • 23
    • 17444382726 scopus 로고    scopus 로고
    • Non Linear Differential Equations with the Caputo Fractional Derivative in the Space of Continuously Differentiable Functions
    • A. A. Kilbas, S.A. Marzan, Non Linear Differential Equations with the Caputo Fractional Derivative in the Space of Continuously Differentiable Functions. Diffrential Equations, 41 (1) (2005), 84-89
    • (2005) Diffrential Equations , vol.41 , Issue.1 , pp. 84-89
    • Kilbas, A.A.1    Marzan, S.A.2
  • 24
    • 38149099031 scopus 로고    scopus 로고
    • Translated from
    • Translated from Differentsial'nye uravneniya. 41 (1) (2005), 82-86.
    • (2005) Differentsial'nye uravneniya , vol.41 , Issue.1 , pp. 82-86
  • 26
    • 51349163878 scopus 로고    scopus 로고
    • Theory of fractional differential equations in a Banach space
    • V. Lakshmikantham and J.V. Devi, Theory of fractional differential equations in a Banach space. Eur. J. Pure Appl. Math. 1 (1) (2008), 38-45.
    • (2008) Eur. J. Pure Appl. Math. , vol.1 , Issue.1 , pp. 38-45
    • Lakshmikantham, V.1    Devi, J.V.2
  • 27
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: Some basic problems in continuum and statistical mechanics
    • (A. Carpinteri, 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, F. Mainardi Eds.), Springer-Verlag, Wien, (1997), 291-348.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 28
    • 0001044887 scopus 로고
    • Relaxation in filled polymers: A fractional calculus approach
    • F. 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, F.1    Schick, W.2    Kilian, H.G.3    Nonnenmacher, T.F.4
  • 30
    • 34848921672 scopus 로고    scopus 로고
    • Some comparison results for integro-fractional differential inequalities
    • S. M. Momani, 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
  • 31
    • 17844385541 scopus 로고    scopus 로고
    • Some analytical properties of solutions of differential equations of noninteger order
    • S. M. Momani, S.B. Hadid, Z.M. Alawenh, Some analytical properties of solutions of differential equations of noninteger order, Int. J. Math. Math. Sci. (2004), 697-701.
    • (2004) Int. J. Math. Math. Sci. , pp. 697-701
    • Momani, S.M.1    Hadid, S.B.2    Alawenh, Z.M.3
  • 32
    • 85025388519 scopus 로고
    • Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
    • H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. 4 (5) (1980), 985-999.
    • (1980) Nonlinear Anal. , vol.4 , Issue.5 , pp. 985-999
    • Mönch, H.1
  • 33
    • 0001571018 scopus 로고
    • On the Cauchy problem for ordinary differential equations in Banach spaces
    • H. Mönch and G. F. Von Harten, On the Cauchy problem for ordinary differential equations in Banach spaces. Archiv. Math. Basel 39 (1982), 153-160.
    • (1982) Archiv. Math. Basel , vol.39 , pp. 153-160
    • Mönch, H.1    von Harten, G.F.2
  • 35
    • 0036650890 scopus 로고    scopus 로고
    • Analogue realizations of fractional-order controllers, in: Fractional Order Calculus and Its Applications
    • I. Podlubny, I. Petraš, B.M. Vinagre, P. O'Leary, L. Dorčak, Analogue realizations of fractional-order controllers, in: Fractional Order Calculus and Its Applications. Nonlinear Dynam. 29 (2002), 281-296.
    • (2002) Nonlinear Dynam. , vol.29 , pp. 281-296
    • Podlubny, I.1    Petraš, I.2    Vinagre, B.M.3    O'Leary, P.4    Dorčak, L.5
  • 36
    • 0002075847 scopus 로고
    • On the application of measure of noncompactness to existence theorems
    • S. Szufla, On the application of measure of noncompactness to existence theorems. Rend. Sem. Mat. Univ. Padova 75 (1986), 1-14.
    • (1986) Rend. Sem. Mat. Univ. Padova , vol.75 , pp. 1-14
    • Szufla, S.1
  • 37
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional diffrential equations
    • S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional diffrential equations. Electron. J. Differential Equations 36 (2006), 1-12.
    • (2006) Electron. J. Differential Equations , vol.36 , pp. 1-12
    • Zhang, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.