Numerical approximations of a dynamic system containing fractional derivatives

Journal of Applied Sciences

Volumn 8, Issue 6, 2008, Pages 1079-1084

  Momani, Shaher ^a   Jaradat, Omar K ^a   Ibrahim, Rabha ^a  

^a MUTAH UNIVERSITY   (Jordan)

Author keywords

Adomian decomposition method; Fractional derivative; Fractional difference method; Pad approximants

Indexed keywords

TECHNOLOGY;

ADOMIAN DECOMPOSITION; ADOMIAN DECOMPOSITION METHOD; APPLIED SCIENCE; APPROXIMANTS; COMPUTABLE COMPONENTS; DIFFERENCE METHOD; FRACTIONAL DERIVATIVES; NUMERICAL APPROXIMATIONS;

NUMERICAL METHODS;

EID: 41949098224     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2008.1079.1084     Document Type: Article

References (23)

1. Abbaoui, K. and Y. Cherruault, 1996a. New ideas for proving convergence of decomposition methods. omput. Math. Appl., 29 (7): 103-108.
2. Abbaoui, K. and Y. Cherruault, 1996b. Convergence of Adomian's method applied to differential equations. Comput. Math. Appl., 28 (5): 103-109.
3. Adomian, G., 1988. A review of the decomposition method in applied mathematics. J. Math. Anal. Applied, 135: 501-544.
4. Adomian, G., 1994. Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston.
5. Baker, G.A., 1975. Essentials of Padé Approximants. Academic Press, London.
6. Boyd, J., 1997. Padé approximants algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domian. Comput. Phys., 11 (3): 299-303.
7. Burden, R.L. and J.D. Faires, 1993. Numerical Analysis. PWS, Boston.
8. Cherruault, Y., 1989. Convergence of Adomian's method. Kybernetes, 18: 31-38.
9. Cherruault, Y. and G. Adomian, 1993. Decomposition methods: A new proof of convergence. Math. Comput. Modelling, 18: 103-106.
10. Grigorenko, I. and E. Grigorenko, 2003. Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett., 91 (3): 034101-034104.
11. He, J.H., 1998a. Nonlinear oscillation with fractional derivative and its applications. International Conference on Vibrating Engineering'98, Dalian, China, pp: 288-291.
12. He, J.H., 1998b. Approximate solution of non linear differential equations with convolution product nonlinearities. Comput Meth. Applied Mech. Eng., 167: 69-73.
13. He, J.H., 1998c. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Meth. Applied Mech. Eng., 167: 57-68.
14. He, J.H., 1999. Variational iteration method-a kind of nonlinear analytical technique: Some examples. Int. J. Nonlin. Mech., 34: 699-708.
15. He, J.H., 2000. Variational iteration method for autonomous ordinary differential systems. Applied Math. Comput., 114 (4-5): 115-123.
16. He, J.H., Y.Q. Wan and Q. Guo, 2004. An iteration formulation for normalized diode characteristics. Int. J. Circuit Theor. Applied, 32 (6): 629-632.
17. Mainardi, F., 1997. Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics. In: Fractals and Fractional Calculus in Continuum Mechanics, Carpinteri, A. and F. Mainardi (Eds.). Springer-Verlag, New York, pp: 291-348.
18. Momani, S., 2004. Analytical approximate solutions of nonlinear oscillators by the modified decomposition method. Int. J. Modern Phys. C., 15 (7): 967-979.
19. Oldham, K.B. and J. Spanier, 1974. The Fractional Calculus. Academic Press, New York.
20. Podlubny, I., 1999. Fractional Differential Equations. Academic Press, New York.
21. Podlubny, I., 2002. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calculus Applied Anal., 5 (4): 367-386.
22. Répaci, A., 1990. Nonlinear dynamical systems: On the accuracy of Adomian's decomposition method. Applied Math. Lett., 3 (3): 35-39.
23. Wazwaz, A.M., 1999. Analytical approximations and Padé approximants for Volterra's population model. Applied Math. Comput, 100 (3): 13-25.