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Volumn 31, Issue 9, 2007, Pages 1907-1914

Numerical approximations and Padé approximants for a fractional population growth model

Author keywords

Adomian decomposition method; Fractional derivative; Pad approximants; Population dynamics; Volterra integral equation

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; POPULATION DYNAMICS;

EID: 34047179962     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2006.06.015     Document Type: Article
Times cited : (61)

References (25)
  • 1
    • 34047133623 scopus 로고    scopus 로고
    • J.H. He, Nonlinear oscillation with fractional derivative and its applications, in: International Conference on Vibrating Engineering, Dalian, China, 1998, pp. 288-291.
  • 2
    • 0347763940 scopus 로고    scopus 로고
    • Some applications of nonlinear fractional differential equations and their approximations
    • He J.H. Some applications of nonlinear fractional differential equations and their approximations. Bull. Sci. Technol. 15 2 (1999) 86-90
    • (1999) Bull. Sci. Technol. , vol.15 , Issue.2 , pp. 86-90
    • He, J.H.1
  • 3
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Eng. 167 (1998) 57-68
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.167 , pp. 57-68
    • He, J.H.1
  • 5
    • 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
  • 6
    • 34047094226 scopus 로고    scopus 로고
    • Population growth in a closed model, Mathematical Modelling: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, PA, 1989
    • Small R.D. Population growth in a closed model, Mathematical Modelling: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, PA, 1989. SIAM Rev. 39 3 (1997) 484-493
    • (1997) SIAM Rev. , vol.39 , Issue.3 , pp. 484-493
    • Small, R.D.1
  • 7
    • 0015020648 scopus 로고
    • Vito Volterra and theoretical ecology
    • Scudo F.M. Vito Volterra and theoretical ecology. Theor. Populat. Biol. 2 (1971) 1-23
    • (1971) Theor. Populat. Biol. , vol.2 , pp. 1-23
    • Scudo, F.M.1
  • 8
    • 0002811385 scopus 로고    scopus 로고
    • Analytical approximations and Padé approximants for Volterra's population model
    • Wazwaz A.M. Analytical approximations and Padé approximants for Volterra's population model. Appl. Math. Comput. 100 (1999) 13-25
    • (1999) Appl. Math. Comput. , vol.100 , pp. 13-25
    • Wazwaz, A.M.1
  • 9
    • 9544231668 scopus 로고    scopus 로고
    • Numerical approximations for population growth models
    • Al-Khaled K. Numerical approximations for population growth models. Appl. Math. Comput. 160 (2005) 865-873
    • (2005) Appl. Math. Comput. , vol.160 , pp. 865-873
    • Al-Khaled, K.1
  • 10
    • 0031238061 scopus 로고    scopus 로고
    • Numerical and analytical solutions of Volterra's population model
    • TeBeest K.G. Numerical and analytical solutions of Volterra's population model. SIAM Rev. 39 3 (1997) 484-493
    • (1997) SIAM Rev. , vol.39 , Issue.3 , pp. 484-493
    • TeBeest, K.G.1
  • 11
    • 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
  • 13
    • 34047176770 scopus 로고    scopus 로고
    • A.Y. 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.
  • 14
    • 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. Astral. Soc. 13 (1967) 529-539
    • (1967) J. Roy. Astral. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 16
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calculus Appl. Anal. 5 (2002) 367-386
    • (2002) Fract. Calculus Appl. Anal. , vol.5 , pp. 367-386
    • Podlubny, I.1
  • 17
    • 0030187555 scopus 로고    scopus 로고
    • Adomian's polynomials for nonlinear operators
    • Seng V., Abbaoui K., and Cherruault Y. Adomian's polynomials for nonlinear operators. Math. Comput. Modell. 24 1 (1996) 59-65
    • (1996) Math. Comput. Modell. , vol.24 , Issue.1 , pp. 59-65
    • Seng, V.1    Abbaoui, K.2    Cherruault, Y.3
  • 18
    • 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
  • 19
    • 0002588102 scopus 로고
    • Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method
    • Rèpaci A. Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method. Appl. Math. Lett. 3 3 (1990) 35-39
    • (1990) Appl. Math. Lett. , vol.3 , Issue.3 , pp. 35-39
    • Rèpaci, A.1
  • 20
    • 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 (1993) 103-106
    • (1993) Math. Comput. Modell. , vol.18 , pp. 103-106
    • Cherruault, Y.1    Adomian, G.2
  • 21
    • 43949159125 scopus 로고    scopus 로고
    • Convergence of Adomian's method applied to differential equations
    • Abbaoui K., and Cherruault Y. Convergence of Adomian's method applied to differential equations. Comput. Math. Appl. 28 5 (1996) 103-109
    • (1996) Comput. Math. Appl. , vol.28 , Issue.5 , pp. 103-109
    • Abbaoui, K.1    Cherruault, Y.2
  • 22
    • 0000487641 scopus 로고    scopus 로고
    • New ideas for proving convergence of decomposition methods
    • Abbaoui K., and Cherruault Y. New ideas for proving convergence of decomposition methods. Comput. Math. Appl. 29 7 (1996) 103-108
    • (1996) Comput. Math. Appl. , vol.29 , Issue.7 , pp. 103-108
    • Abbaoui, K.1    Cherruault, Y.2
  • 24
    • 0001100804 scopus 로고    scopus 로고
    • Padè approximants algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain
    • Boyd J. Padè approximants algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput. Phys. 11 3 (1997) 299-303
    • (1997) Comput. Phys. , vol.11 , Issue.3 , pp. 299-303
    • Boyd, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.