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Volumn 182, Issue 1, 2006, Pages 761-770

A numerical scheme for the solution of multi-order fractional differential equations

Author keywords

Decomposition method; Fractional differential equations; Multi order equations

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS;

EID: 33750901303     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.04.037     Document Type: Article
Times cited : (44)

References (25)
  • 1
    • 0041185368 scopus 로고
    • A review of the decomposition method in applied mathematics
    • Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135 (1988) 501-544
    • (1988) J. Math. Anal. Appl. , vol.135 , pp. 501-544
    • Adomian, G.1
  • 3
    • 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. J. Appl. Mech. 51 (1984) 294-298
    • (1984) J. Appl. Mech. , vol.51 , pp. 294-298
    • Bagley, R.L.1    Torvik, P.J.2
  • 4
    • 0042639049 scopus 로고
    • Stability barriers to the construction of ρ, σ-reducible and fractional quadrautre rules
    • Numerical Integration III. BraB H., and Hammerlin B.G. (Eds), Birkhauser, Basel
    • Baker C.T.H., and Derakhshan M.S. Stability barriers to the construction of ρ, σ-reducible and fractional quadrautre rules. In: BraB H., and Hammerlin B.G. (Eds). Numerical Integration III. Ser. Numer. Math vol. 85 (1988), Birkhauser, Basel 1-15
    • (1988) Ser. Numer. Math , vol.85 , pp. 1-15
    • Baker, C.T.H.1    Derakhshan, M.S.2
  • 5
    • 33750930024 scopus 로고    scopus 로고
    • L. Blank, Numerical treatment of differential equations of fractional order, MCCM Numerical Analysis Report No. 287, The University of Manchester, 1996.
  • 6
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J. Roy. Astr. Soc. 13 (1967) 529-539
    • (1967) J. Roy. Astr. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 7
    • 84970868898 scopus 로고
    • Convergence of Adomian's method
    • Cherruault Y. Convergence of Adomian's method. Kybernetes 18 (1989) 31-38
    • (1989) Kybernetes , vol.18 , pp. 31-38
    • Cherruault, Y.1
  • 8
    • 0000395259 scopus 로고
    • Decomposition methods: a new proof of convergence
    • Cherruault Y., and Adomian G. Decomposition methods: a new proof of convergence. Math. Comput. Modell. 18 12 (1993) 103-106
    • (1993) Math. Comput. Modell. , vol.18 , Issue.12 , pp. 103-106
    • Cherruault, Y.1    Adomian, G.2
  • 9
    • 0001618393 scopus 로고    scopus 로고
    • An alogrithm for the numerical solution of differential equations of fractional order
    • Diethelm K. An alogrithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Ana. 5 (1997) 1-6
    • (1997) Electron. Trans. Numer. Ana. , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 10
    • 0012899160 scopus 로고    scopus 로고
    • Numerical solution of the Bagley-Torvik equation
    • Diethelm K., and Ford N.J. Numerical solution of the Bagley-Torvik equation. BIT 42 (2002) 490-507
    • (2002) BIT , vol.42 , pp. 490-507
    • Diethelm, K.1    Ford, N.J.2
  • 11
    • 0037113861 scopus 로고    scopus 로고
    • Multi-order fractional differential equations and their numerical solution
    • Diethelm K., and Ford N.J. Multi-order fractional differential equations and their numerical solution. Appl. Math. Comput. 148 (2002) 401-418
    • (2002) Appl. Math. Comput. , vol.148 , pp. 401-418
    • Diethelm, K.1    Ford, N.J.2
  • 13
    • 33748663764 scopus 로고    scopus 로고
    • Numerical solution of linear multi-term differential equations of fractional order
    • Diethelm K., and Luchko Y. Numerical solution of linear multi-term differential equations of fractional order. J. Comput. Anal. Appl. 6 (2004) 243-263
    • (2004) J. Comput. Anal. Appl. , vol.6 , pp. 243-263
    • Diethelm, K.1    Luchko, Y.2
  • 14
    • 0037113861 scopus 로고    scopus 로고
    • The numerical solution of linear multi-term fractional differential equations: systems of equations
    • Edwards J.T., Ford N.J., and Simpson A.C. The numerical solution of linear multi-term fractional differential equations: systems of equations. J. Comput. Appl. Math. 148 (2002) 401-418
    • (2002) J. Comput. Appl. Math. , vol.148 , pp. 401-418
    • Edwards, J.T.1    Ford, N.J.2    Simpson, A.C.3
  • 15
    • 9744276851 scopus 로고    scopus 로고
    • Numerical methods for multi-term fractional (arbitrary) orders differential equations
    • El-Mesiry A.E.M., El-Sayed A.M.A., and El-Saka H.A.A. Numerical methods for multi-term fractional (arbitrary) orders differential equations. Appl. Math. Comput. 160 (2005) 683-699
    • (2005) Appl. Math. Comput. , vol.160 , pp. 683-699
    • El-Mesiry, A.E.M.1    El-Sayed, A.M.A.2    El-Saka, H.A.A.3
  • 16
    • 84966227123 scopus 로고
    • Fractional linear multistep methods for Abel-Volterra integral equations of the second kind
    • Lubich C. Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Math. Comput. 45 (1985) 463-469
    • (1985) Math. Comput. , vol.45 , pp. 463-469
    • Lubich, C.1
  • 17
    • 33750908699 scopus 로고    scopus 로고
    • AY. Luchko, R. Groreflo, The initial value problem for some fractional differential equations with the Caputo derivative, Preprint series A08-98, Fachbreich Mathematik und Informatik, Freic Universitat Berlin, 1998.
  • 18
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: some basic problems in continuum and statistical mechanics
    • carpinteri A., and Mainardi F. (Eds), Springer-Verlag, New York
    • Mainardi F. Fractional calculus: some basic problems in continuum and statistical mechanics. In: carpinteri A., and Mainardi F. (Eds). Fractals and Fractional calculus in continuum Mechanics (1997), Springer-Verlag, New York 291-348
    • (1997) Fractals and Fractional calculus in continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 20
    • 12244291039 scopus 로고    scopus 로고
    • Numerical solutions for systems of fractional differential equations by the decomposition method
    • Momani S., and Al-Khaled K. Numerical solutions for systems of fractional differential equations by the decomposition method. Appl. Math. Comput. 162 3 (2005) 1351-1365
    • (2005) Appl. Math. Comput. , vol.162 , Issue.3 , pp. 1351-1365
    • Momani, S.1    Al-Khaled, K.2
  • 24
    • 0002588102 scopus 로고
    • Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method
    • Répaci A. Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method. Appl. Math. Lett. 3 4 (1990) 35-39
    • (1990) Appl. Math. Lett. , vol.3 , Issue.4 , pp. 35-39
    • Répaci, A.1
  • 25
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Appl. Math. Comput. 131 2 (2002) 517-529
    • (2002) Appl. Math. Comput. , vol.131 , Issue.2 , pp. 517-529
    • Shawagfeh, N.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.