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Volumn 148, Issue 2, 2002, Pages 401-418

The numerical solution of linear multi-term fractional differential equations: Systems of equations

Author keywords

Fractional differential equations; Multi term equations; Numerical methods

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING;

EID: 0037113861     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00558-7     Document Type: Article
Times cited : (179)

References (19)
  • 1
    • 0004171153 scopus 로고    scopus 로고
    • Numerical treatment of differential equations of fractional order
    • Manchester Centre for Computational Mathematics
    • L. Blank, Numerical treatment of differential equations of fractional order, Numerical Analysis Report 287, Manchester Centre for Computational Mathematics, 1996.
    • (1996) Numerical Analysis Report 287
    • Blank, L.1
  • 2
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent II
    • M. Caputo, Linear models of dissipation whose Q is almost frequency independent II, Geophys. J. Royal Astron. Soc. 13 (1967) 529-539.
    • (1967) Geophys. J. Royal Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 3
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Kent State University, ETNA 5
    • K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, in: Electronic Transactions on Numerical Analysis, Vol. 5, Kent State University, ETNA 5 (1997) pp. 1-6.
    • (1997) Electronic Transactions on Numerical Analysis , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 4
    • 0031477557 scopus 로고    scopus 로고
    • Numerical approximation of finite-part integrals with generalised compound quadrature formulae
    • K. Diethelm, Numerical approximation of finite-part integrals with generalised compound quadrature formulae, IMA J. Numer. Anal. 17 (1997) 479-493.
    • (1997) IMA J. Numer. Anal. , vol.17 , pp. 479-493
    • Diethelm, K.1
  • 5
    • 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
  • 6
    • 0012899160 scopus 로고    scopus 로고
    • Numerical solution of the Bagley-Torvik equation
    • K. Diethelm, N.J. Ford, 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
  • 7
    • 0012899161 scopus 로고    scopus 로고
    • The numerical solution of linear and nonlinear fractional differential equations involving fractional derivatives of several orders
    • Manchester Centre for Computational Mathematics
    • K. Diethelm, N.J. Ford, The numerical solution of linear and nonlinear fractional differential equations involving fractional derivatives of several orders, Numerical Analysis Report 379, Manchester Centre for Computational Mathematics, 2001.
    • (2001) Numerical Analysis Report 379
    • Diethelm, K.1    Ford, N.J.2
  • 8
    • 0012897479 scopus 로고    scopus 로고
    • Numerical solution of linear multi-term differential equations of fractional order
    • to appear
    • K. Diethelm, Y. Luchko, Numerical solution of linear multi-term differential equations of fractional order, J. Comput. Anal. Appl., to appear.
    • J. Comput. Anal. Appl.
    • Diethelm, K.1    Luchko, Y.2
  • 9
    • 0035625795 scopus 로고    scopus 로고
    • The numerical solution of fractional differential equations: Speed versus accuracy
    • N.J. Ford, A.C. Simpson, The numerical solution of fractional differential equations: speed versus accuracy, Numer. Algorithms 26.4 (2001) 333-346.
    • (2001) Numer. Algorithms , vol.26 , Issue.4 , pp. 333-346
    • Ford, N.J.1    Simpson, A.C.2
  • 10
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus: Integral and differential equations of fractional order
    • A. Carpinteri, F. Mainardi (Eds.), Springer, Berlin
    • R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Berlin, 1997, pp. 223-276.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 12
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • C. Lubich, 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
  • 13
    • 34250092484 scopus 로고
    • Convolution quadrature and discretized operational calculus, I
    • C. Lubich, Convolution quadrature and discretized operational calculus, I, Numer. Math. 52 (1988) 129-145.
    • (1988) Numer. Math. , vol.52 , pp. 129-145
    • Lubich, C.1
  • 14
    • 0001983732 scopus 로고    scopus 로고
    • Some basic problems in continuum and statistical mechanics
    • A. Carpinteri, F. Mainardi (Eds.), Springer, Berlin
    • F. Mainardi, Some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer, Berlin, 1997, pp. 291-348.
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 19
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • P.J. Torvik, R.L. Bagley, 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
    • Torvik, P.J.1    Bagley, R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.