Analytical approximations for a population growth model with fractional order

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 5, 2009, Pages 1978-1983

  Xu, Hang ^a  

^a Shanghai Jiao Tong University   (China)

Author keywords

Analytical approximations; Caputo fractional derivative; Homotopy analysis method; Nonlinear fractional differential equation

Indexed keywords

DIFFERENTIATION (CALCULUS); INTEGRODIFFERENTIAL EQUATIONS; POPULATION STATISTICS;

ANALYSIS METHOD; ANALYTICAL APPROXIMATION; CAPUTO FRACTIONAL DERIVATIVES; FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION; FRACTIONAL ORDER; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS; POPULATION GROWTH MODELS; VOLTERRA MODEL;

NONLINEAR EQUATIONS;

EID: 56049105387     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2008.07.006     Document Type: Article

References (12)

1. Scudo F.M. Vito volterra and theoretical ecology. Theoret Population Biol 2 (1971) l-23
2. Small RD. Population growth in a closed model. Mathematical modelling: classroom notes in applied mathematics. Philadelphia, PA: SIAM; 1989.
3. TeBeest K.G. Numerical and analytical solutions of Volterra population model. SIAM Rev 39 (1997) 484-493
4. Wazwaz A.M., and Khuri S.A. Two methods for solving integral equations. Appl Math Comput 77 (1996) 79-89
5. Liao S.J. Beyond Perturbation: Introduction to the Homotopy Analysis Method (2003), Chapman and Hall/CRC Press, Boca Raton
6. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers., Boston
7. Momani S., and Qaralleh R. Numerical approximations and Padé approximants for a fractional population growth model. Appl Math Modelling 31 (2007) 1907-1914
8. Liao SJ. The proposed homotopy analysis techniques for the solution of nonlinear problems. PhD Dissertation (in English). Shanghai: Shanghai Jiao Tong University; 1992.
9. Xu H., and Liao S.J. Analytic solutions of magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate. J Non-Newton Fluid Mech 159 (2005) 46-55
10. Podlubny I. Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications (1999), Academic Press, SanDiego
11. Caputo M. Linear models of dissipation whose q is almost frequency independent. Part II. Geophys J R Astr Soc 13 (1967) 529-539
12. Cang J, Tan Y, Xu H, Liao SJ. Series solutions of non-linear Riccati differential equations with fractional order. Chaos Soliton Fract, in press.