메뉴 건너뛰기




Volumn 16, Issue 4, 2011, Pages 2086-2097

The existence of multiple positive solutions for boundary value problems of nonlinear fractional differential equations

Author keywords

Boundary value problem; Fixed point theorem; Fractional differential equation; Fractional Green's function; Lower and upper solution method; Positive solution

Indexed keywords

FIXED POINT ARITHMETIC; FUNCTIONAL ANALYSIS; NONLINEAR EQUATIONS; TOPOLOGY;

EID: 78049442199     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.08.017     Document Type: Article
Times cited : (146)

References (30)
  • 5
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Larange equations for fractional variational problems
    • Agarwal R.P. Formulation of Euler-Larange equations for fractional variational problems. J Math Anal Appl 2002, 272:368-379.
    • (2002) J Math Anal Appl , vol.272 , pp. 368-379
    • Agarwal, R.P.1
  • 7
    • 70350367184 scopus 로고    scopus 로고
    • Fractional calculus in viscoelasticity: An experimental study
    • Meral F.C., Royston T.J., Magin R. Fractional calculus in viscoelasticity: An experimental study. Commun Nonlinear Sci Numer Simul 2010, 15(4):939-945.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , Issue.4 , pp. 939-945
    • Meral, F.C.1    Royston, T.J.2    Magin, R.3
  • 9
    • 0030528474 scopus 로고    scopus 로고
    • Existence and uniqueness for a nonlinear fractional differential equation
    • Delbosco D., Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J Math Anal Appl 1996, 204:609-625.
    • (1996) J Math Anal Appl , vol.204 , pp. 609-625
    • Delbosco, D.1    Rodino, L.2
  • 10
    • 0034670545 scopus 로고    scopus 로고
    • The existence of a positive solution for nonlinear fractional differential equation
    • Zhang S. The existence of a positive solution for nonlinear fractional differential equation. J Math Anal Appl 2000, 252:804-812.
    • (2000) J Math Anal Appl , vol.252 , pp. 804-812
    • Zhang, S.1
  • 11
    • 0037308989 scopus 로고    scopus 로고
    • Existence of positive solutions for some class of nonlinear fractional equation
    • Zhang S. Existence of positive solutions for some class of nonlinear fractional equation. J Math Anal Appl 2003, 278:136-148.
    • (2003) J Math Anal Appl , vol.278 , pp. 136-148
    • Zhang, S.1
  • 13
    • 77952705214 scopus 로고    scopus 로고
    • A collocation-shooting method for solving fractional boundary value problems
    • Al-Mdallal M., Syam M.I., Anwar M.N. A collocation-shooting method for solving fractional boundary value problems. Commun Nonlinear Sci Numer Simul 2010, 15(12):3814-3822.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , Issue.12 , pp. 3814-3822
    • Al-Mdallal, M.1    Syam, M.I.2    Anwar, M.N.3
  • 14
    • 33748963091 scopus 로고    scopus 로고
    • Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method
    • Jafari H., Daftardar-Gejji V. Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method. Appl Math Comput 2006, 180:700-706.
    • (2006) Appl Math Comput , vol.180 , pp. 700-706
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 15
    • 68949086378 scopus 로고    scopus 로고
    • Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations
    • Article ID 494720
    • Ahmad B., Nieto J.J. Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations. Abst Appl Anal 2009, Article ID 494720.
    • (2009) Abst Appl Anal
    • Ahmad, B.1    Nieto, J.J.2
  • 16
    • 70249121999 scopus 로고    scopus 로고
    • Existence of periodic solution for a nonlinear fractional differential equation
    • Article ID 324561
    • Belmekki M., Nieto J.J., Rodríguez-López R. Existence of periodic solution for a nonlinear fractional differential equation. Boundary Value Problems 2009, Article ID 324561.
    • (2009) Boundary Value Problems
    • Belmekki, M.1    Nieto, J.J.2    Rodríguez-López, R.3
  • 17
    • 85071293086 scopus 로고    scopus 로고
    • Existence of positive solutions for singular fractional equations
    • Qiu T., Bai Z. Existence of positive solutions for singular fractional equations. Electron J Differ Equat 2008, 146:1-9.
    • (2008) Electron J Differ Equat , vol.146 , pp. 1-9
    • Qiu, T.1    Bai, Z.2
  • 18
    • 77956856109 scopus 로고    scopus 로고
    • Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems
    • Article ID 421310
    • Mena J.C., Harjani J., Sadarangani K. Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems. Boundary Value Problems 2009, Article ID 421310.
    • (2009) Boundary Value Problems
    • Mena, J.C.1    Harjani, J.2    Sadarangani, K.3
  • 19
    • 68949184371 scopus 로고    scopus 로고
    • Singular positone and semipositone boundary value problems of nonlinear fractional differential equations
    • Article ID 535209
    • Yuan C., Jiang D., Xu X. Singular positone and semipositone boundary value problems of nonlinear fractional differential equations. Math Prob Eng 2009, Article ID 535209.
    • (2009) Math Prob Eng
    • Yuan, C.1    Jiang, D.2    Xu, X.3
  • 20
    • 71649090846 scopus 로고    scopus 로고
    • The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application
    • Jiang D., Yuan C. The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application. Nonlinear Anal 2009, 72:710-719.
    • (2009) Nonlinear Anal , vol.72 , pp. 710-719
    • Jiang, D.1    Yuan, C.2
  • 21
    • 70350123911 scopus 로고    scopus 로고
    • Upper and lower solutions method and a fractional differential equation boundary value problem
    • Shi A., Zhang S. Upper and lower solutions method and a fractional differential equation boundary value problem. Electron J Qual Theor Differ Equat 2009, 30:1-13.
    • (2009) Electron J Qual Theor Differ Equat , vol.30 , pp. 1-13
    • Shi, A.1    Zhang, S.2
  • 22
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Bai Z., Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J Math Anal Appl 2005, 311:495-505.
    • (2005) J Math Anal Appl , vol.311 , pp. 495-505
    • Bai, Z.1    Lü, H.2
  • 23
    • 33645152919 scopus 로고    scopus 로고
    • Positive solutions for boundary-value problems of nonlinear fractional differential equations
    • Zhang S. Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron J Differ Equat 2006, 36:1-12.
    • (2006) Electron J Differ Equat , vol.36 , pp. 1-12
    • Zhang, S.1
  • 24
    • 68349091496 scopus 로고    scopus 로고
    • Positive solutions for boundary value problems of nonlinear fractional differential equation
    • Liang S., Zhang J. Positive solutions for boundary value problems of nonlinear fractional differential equation. Nonlinear Anal 2009, 71:5545-5550.
    • (2009) Nonlinear Anal , vol.71 , pp. 5545-5550
    • Liang, S.1    Zhang, J.2
  • 25
    • 67651094005 scopus 로고    scopus 로고
    • Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation
    • Xu X., Jiang D., Yuan C. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Nonlinear Anal 2009, 71(10):4676-4688.
    • (2009) Nonlinear Anal , vol.71 , Issue.10 , pp. 4676-4688
    • Xu, X.1    Jiang, D.2    Yuan, C.3
  • 26
    • 36248933572 scopus 로고    scopus 로고
    • Positive solutions for boundary value problems of nonlinear fractional differential equation
    • Article ID 10368
    • El-Shahed M. Positive solutions for boundary value problems of nonlinear fractional differential equation. Abs Appl Anal 2007, Article ID 10368.
    • (2007) Abs Appl Anal
    • El-Shahed, M.1
  • 28
    • 0000394603 scopus 로고
    • Multiple positive fixed points of nonlinear operators on ordered Banach spaces
    • Leggett R.W., Williams L.R. Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana Univ Math J 1979, 28:673-688.
    • (1979) Indiana Univ Math J , vol.28 , pp. 673-688
    • Leggett, R.W.1    Williams, L.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.