Adomian decomposition method and non-analytical solutions of fractional differential equations

Romanian Reports of Physics

Volumn 56, Issue 7-8, 2011, Pages 873-880

  Wu, Guo Cheng ^a,b   Shi, Yong Guo ^a,b   Wu, Kai Teng ^a,b  

^a Key Laboratory of Numerical Simulation of Sichuan Province   (China)

^b NEIJIANG NORMAL UNIVERSITY   (China)

Author keywords

Adomian decomposition method; Fractional differential equations; Fractional taylor series

Indexed keywords

EID: 80053143209     PISSN: 1221146X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. K.M. Kolwankar, A.D. Gangal, Fractional differentiability of nowhere differentiable functions and dimensions, Chaos, 6, 505-513 (1996).
2. K.M. Kolwankar, A.D. Gangal, Holder exponents of irregular signals and local fractional derivatives, Pramana. J. Phys. 48, 49-68 (1997).
3. K.M. Kolwankar, A.D. Gangal, Local fractional Fokker-Planck equation, Phys. Rev. Lett. 80, 214-21 (1998).
4. N.T. Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput. 131, 517-529 (2002).
5. Y. Chen, H.L. An, Numerical solutions of coupled Burgers equations with time-space fractional derivatives, Appl. Math. Comput. 200, 87-95 (2008).
6. C.P. Li, Y. H. Wang, Numerical algorithm based on Adomian decomposition for fractional differential equations, Comput. Math. Appl. 57, 1672-1681 (2009).
7. Z. Odibat, S. Momani, A generalized differential transform method for linear partial differential equations of fractional order. Appl. Math. Lett. 21, 194-199 (2008).
8. G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results, Comput. Math. Appl. 51, 1367-1376 (2006).
9. Y. Chen, Y. Yan, K.W. Zhang, On the local fractional derivative, J. Math. Anal. Appl. 362, 17-33 (2010).
10. A. Carpinteri, P. Cornetti, A fractional calculus approach to the description of stress and strain localization in fractal media, Chaos Solitons Fract. 13, 85-94 (2002).
11. α, Appl. Math. Lett. 18, 739-748 (2005).
12. G. Jumarie, Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferentiable functions, Chaos Solitons Fract. 32, 969-987 (2007).
13. G. Jumarie, Laplace's transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative, Appl. Math. Lett. 22, 1659-1664 (2009).
14. R. Almeida, A.B. Malinowska, D. F. M. Torres, A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String, J. Math. Phys. 51, 033503 (2010).
15. G.C. Wu, A Fractional Lie Group Method for Anomalous Diffusion Equations, Commun. Frac. Calc. 1, 27-31(2010).
16. G.C. Wu, E.W.M. Lee, Fractional Variational Iteration Method and Its Application, Phys. Lett. A 374, 2506-2509 (2010).
17. G.C. Wu, Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations, Comput. Math. Appl., accepted.
18. Z.G. Deng, G.C. Wu, Approximate solution of fractional differential equations with uncertainty, Rom. J. Phys., accepted.
19. G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501-544 (1988).
20. G. Adomian, R. Rach, Transformation of series, Appl. Math. Lett. 4, 69-71 (1991).
21. J.S. Duan, Recurrence triangle for Adomian polynomials, Appl. Math. Comput. 216, 1235-1241 (2010);
22. J.S. Duan, An efficient algorithm for the multivariable Adomian polynomials, Appl. Math. Comput., accepted.
23. S. Saha Ray, R.K. Bera, An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method, Appl. Math. Comput. 167, 561-571 (2005).
24. J.R. Dormand, P.J. Prince, A family of embedded Runge-Kutta formulae, J. Comp. Appl. Math. 6, 19-26, (1980).