메뉴 건너뛰기




Volumn 15, Issue 12, 2010, Pages 3814-3822

A collocation-shooting method for solving fractional boundary value problems

Author keywords

Bagley Torvik equation; Collocation method; Shooting method

Indexed keywords

COMPUTATIONAL METHODS;

EID: 77952705214     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.01.020     Document Type: Article
Times cited : (117)

References (35)
  • 1
    • 34247477202 scopus 로고    scopus 로고
    • On fractional order differential equations model for nonlocal epidemics
    • Ahmed E., and Elgazzar A.S. On fractional order differential equations model for nonlocal epidemics. Phys A 379 2 (2007) 607-614
    • (2007) Phys A , vol.379 , Issue.2 , pp. 607-614
    • Ahmed, E.1    Elgazzar, A.S.2
  • 2
    • 33750295344 scopus 로고    scopus 로고
    • Equilibrium points, stability, and numerical solutions of fractional-order predator-prey and rabies models
    • Ahmed E., El-Sayed A.M.A., and Elsaka H.A.A. Equilibrium points, stability, and numerical solutions of fractional-order predator-prey and rabies models. J Math Anal Appl 325 1 (2007) 542-553
    • (2007) J Math Anal Appl , vol.325 , Issue.1 , pp. 542-553
    • Ahmed, E.1    El-Sayed, A.M.A.2    Elsaka, H.A.A.3
  • 3
    • 64549120203 scopus 로고    scopus 로고
    • An efficient method for solving fractional Sturm-Liouville problems
    • Al-Mdallal Q.M. An efficient method for solving fractional Sturm-Liouville problems. Chaos, Solitons Fractals 40 1 (2009) 183-189
    • (2009) Chaos, Solitons Fractals , vol.40 , Issue.1 , pp. 183-189
    • Al-Mdallal, Q.M.1
  • 4
    • 85196150117 scopus 로고    scopus 로고
    • On the numerical solution of fractional Sturm-Liouville problems
    • Al-Mdallal Q.M. On the numerical solution of fractional Sturm-Liouville problems. Int J Comput Math 99999 (2009) 1
    • (2009) Int J Comput Math , vol.99999 , pp. 1
    • Al-Mdallal, Q.M.1
  • 5
    • 35248854592 scopus 로고    scopus 로고
    • Efficient shooting method for solving two point boundary value problems
    • Attili B., and Syam M. Efficient shooting method for solving two point boundary value problems. Chaos, Solitons Fractals 35 5 (2008) 895-903
    • (2008) Chaos, Solitons Fractals , vol.35 , Issue.5 , pp. 895-903
    • Attili, B.1    Syam, M.2
  • 7
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Bagley R.L., and Torvik P.J. On the appearance of the fractional derivative in the behavior of real materials. ASME J Appl Mech 51 2 (1984) 294-298
    • (1984) ASME J Appl Mech , vol.51 , Issue.2 , pp. 294-298
    • Bagley, R.L.1    Torvik, P.J.2
  • 8
    • 84981825145 scopus 로고
    • Definition of physically consistent damping laws with fractional derivatives
    • Beyer H., and Kempfle S. Definition of physically consistent damping laws with fractional derivatives. Zeitschrift fr Angewandte Mathematik und Mechanik 75 8 (1995) 623-635
    • (1995) Zeitschrift fr Angewandte Mathematik und Mechanik , vol.75 , Issue.8 , pp. 623-635
    • Beyer, H.1    Kempfle, S.2
  • 9
    • 0004171153 scopus 로고    scopus 로고
    • Numerical treatment of differential equations of fractional order
    • Manchester Center for Numerical Computational Mathematics;
    • Blank L. Numerical treatment of differential equations of fractional order. Numerical Analysis Report 287, Manchester Center for Numerical Computational Mathematics; 1996.
    • (1996) Numerical Analysis Report , vol.287
    • Blank, L.1
  • 10
    • 10344238128 scopus 로고    scopus 로고
    • Adomian decomposition: a tool for solving a system of fractional differential equations
    • Daftardar-Geiji V., and Jafari H. Adomian decomposition: a tool for solving a system of fractional differential equations. J Math Anal Appl 301 2 (2005) 508-518
    • (2005) J Math Anal Appl , vol.301 , Issue.2 , pp. 508-518
    • Daftardar-Geiji, V.1    Jafari, H.2
  • 11
    • 33845961350 scopus 로고    scopus 로고
    • Analysis of a system of nonautonomous fractional differential equations involving Capato derivatives
    • Daftardar-Geiji V., and Jafari H. Analysis of a system of nonautonomous fractional differential equations involving Capato derivatives. J Math Anal Appl 328 (2007) 1026-1033
    • (2007) J Math Anal Appl , vol.328 , pp. 1026-1033
    • Daftardar-Geiji, V.1    Jafari, H.2
  • 12
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Diethelm K. An algorithm for the numerical solution of differential equations of fractional order. Elect Translat Numer Anal 5 (1997) 1-6
    • (1997) Elect Translat Numer Anal , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 13
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam 29 (2002) 3-22
    • (2002) Nonlinear Dynam , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 14
    • 54549122514 scopus 로고    scopus 로고
    • Applications of He's variational iteration method to solve semidifferential equations of nth order
    • Ghorbani A., and Alavi A. Applications of He's variational iteration method to solve semidifferential equations of nth order. Math Prob Eng 2008 (2008) 1-9
    • (2008) Math Prob Eng , vol.2008 , pp. 1-9
    • Ghorbani, A.1    Alavi, A.2
  • 15
    • 0035500967 scopus 로고    scopus 로고
    • A nonlinear shooting method for two point boundary value problems
    • Ha S.N. A nonlinear shooting method for two point boundary value problems. Comput Math Appl 42 (2001) 1411-1420
    • (2001) Comput Math Appl , vol.42 , pp. 1411-1420
    • Ha, S.N.1
  • 18
    • 46049100549 scopus 로고    scopus 로고
    • A fractional-order implicit difference approximation for the space-time fractional diffusion equation
    • Liw F., Zhuang P., Anh V., and Turner J. A fractional-order implicit difference approximation for the space-time fractional diffusion equation. ANZJAMJ 47 (2006) C48-C68
    • (2006) ANZJAMJ , vol.47
    • Liw, F.1    Zhuang, P.2    Anh, V.3    Turner, J.4
  • 19
    • 51349139941 scopus 로고    scopus 로고
    • Theory of fractional functional differential equations
    • Lakshmikantham V. Theory of fractional functional differential equations. Nonlinear Anal: Theory, Meth Appl 69 10 (2008) 3337-3343
    • (2008) Nonlinear Anal: Theory, Meth Appl , vol.69 , Issue.10 , pp. 3337-3343
    • Lakshmikantham, V.1
  • 20
    • 45049084850 scopus 로고    scopus 로고
    • General uniqueness and monotone iterative technique for fractional differential equations
    • Lakshmikantham V., and Vatsala A.S. General uniqueness and monotone iterative technique for fractional differential equations. Appl. Math. Letters 21 8 (2008) 828-834
    • (2008) Appl. Math. Letters , vol.21 , Issue.8 , pp. 828-834
    • Lakshmikantham, V.1    Vatsala, A.S.2
  • 21
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich C. Discretized fractional calculus. SIAM J Math Anal 17 3 (1986) 704-719
    • (1986) SIAM J Math Anal , vol.17 , Issue.3 , pp. 704-719
    • Lubich, C.1
  • 22
    • 34250094006 scopus 로고
    • Convoluton quadrature and discretized operational calculus (part II)
    • Lubich C. Convoluton quadrature and discretized operational calculus (part II). Numerisch Mathematik 52 4 (1988) 413-425
    • (1988) Numerisch Mathematik , vol.52 , Issue.4 , pp. 413-425
    • Lubich, C.1
  • 23
    • 0038445397 scopus 로고
    • Fractional relaxiation and fractional diffusion equations: Mathematical aspects
    • Mainardi F. Fractional relaxiation and fractional diffusion equations: mathematical aspects. In: Proceedings of the 14th IMACS world congress, vol. 1; 1994. p. 329-32.
    • (1994) Proceedings of the 14th IMACS world congress , vol.1 , pp. 329-332
    • Mainardi, F.1
  • 24
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solution for the fractional diffusion-wave equation
    • Mainardi F. The fundamental solution for the fractional diffusion-wave equation. Appl Math Lett 9 6 (1996) 23-28
    • (1996) Appl Math Lett , vol.9 , Issue.6 , pp. 23-28
    • Mainardi, F.1
  • 25
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion-wave phenomena
    • Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solutions Fractals 7 (1996) 1461-1477
    • (1996) Chaos, Solutions Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 26
    • 3042930667 scopus 로고
    • Derivatives of noninteger order and their applications
    • Michalski M.W. Derivatives of noninteger order and their applications. Dissertationes Mathematicae 328 (1993) 1-47
    • (1993) Dissertationes Mathematicae , vol.328 , pp. 1-47
    • Michalski, M.W.1
  • 28
    • 36549063424 scopus 로고    scopus 로고
    • A generalized differential transform for linear partial differential equations of fractional order
    • Obaidat Z., and Momani S. A generalized differential transform for linear partial differential equations of fractional order. Appl Math Lett 21 (2008) 194-199
    • (2008) Appl Math Lett , vol.21 , pp. 194-199
    • Obaidat, Z.1    Momani, S.2
  • 29
    • 0027146124 scopus 로고
    • Representation of the absorption of nonlinear waves by fractional derivatives
    • Ochmann M., and Makarov S. Representation of the absorption of nonlinear waves by fractional derivatives. J Acoust Soc Am 94 6 (1993) 3392-3399
    • (1993) J Acoust Soc Am , vol.94 , Issue.6 , pp. 3392-3399
    • Ochmann, M.1    Makarov, S.2
  • 31
    • 25644439033 scopus 로고    scopus 로고
    • Analytical solution of the Bagley Torvik equation by Adomian decomposition method
    • Saha Ray S., and Bera R.K. Analytical solution of the Bagley Torvik equation by Adomian decomposition method. Appl Math Comput 168 (2005) 398-410
    • (2005) Appl Math Comput , vol.168 , pp. 398-410
    • Saha Ray, S.1    Bera, R.K.2
  • 32
    • 33748915280 scopus 로고    scopus 로고
    • Existence of solution for a boundary value problem of fractional order
    • Shuqin Z. Existence of solution for a boundary value problem of fractional order. Acta Mathematica Scientia 26B 2 (2006) 220-228
    • (2006) Acta Mathematica Scientia , vol.26 B , Issue.2 , pp. 220-228
    • Shuqin, Z.1
  • 33
    • 55649098198 scopus 로고    scopus 로고
    • Boundary value problems for a coupled system of nonlinear fractional differential equations
    • Su X. Boundary value problems for a coupled system of nonlinear fractional differential equations. Appl Math Lett 22 (2009) 64-69
    • (2009) Appl Math Lett , vol.22 , pp. 64-69
    • Su, X.1
  • 34
    • 33644585616 scopus 로고    scopus 로고
    • Numerical solution of semidifferential equation by collocation method
    • Rawashdeh E.A. Numerical solution of semidifferential equation by collocation method. Appl Math Comput 174 (2006) 869-876
    • (2006) Appl Math Comput , vol.174 , pp. 869-876
    • Rawashdeh, E.A.1
  • 35
    • 33750820240 scopus 로고    scopus 로고
    • Adomian decomposition method for solving fractional nonlinear differential equations
    • El-Wakil S., Elhambaly A., and Abdou M.A. Adomian decomposition method for solving fractional nonlinear differential equations. Appl Math Comput 182 (2006) 313-324
    • (2006) Appl Math Comput , vol.182 , pp. 313-324
    • El-Wakil, S.1    Elhambaly, A.2    Abdou, M.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.