Analytic approximations for fractional-order hyperchaotic system

Journal of Advanced Research in Dynamical and Control Systems

Volumn 3, Issue 3, 2012, Pages 1-12

  Mohamed, Mohamed S ^a,b   Ghany, Hossam A ^c  

^a TAIF UNIVERSITY   (Saudi Arabia)

^b Al Azhar University   (Egypt)

^c Helwan University   (Egypt)

Author keywords

Caputo's fractional derivative; Fractional order hyperchaotic system; Homotopy analysis method; Hyperchaotic system

Indexed keywords

EID: 84864244828     PISSN: None     EISSN: 1943023X     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. A.K. Alomari, M.S.M. Noorani, R. Nazar, C.P. Li. Homotopy analysis method for solving fractional Lorenz system. Commun Nonlinear Sci. Numer. Simul., 2010, 15: 1864-1872, doi: 10.1016/j.cnsns.2009.08.005.
2. M.M. Al-Sawalha, M.S. Noorani. Numerical experiments on the hyperchaotic Chen system by the Adomian decomposition method. Int. J. Comput. Methods. 2008, 5: 403-412.
3. M.M. Al-Sawalha, M.S. Noorani, I. Hashim. On accuracy of Adomian decomposition method for hyperchaotic Rossler system. Chaos, Solitons & Fractals, 2009, 40: 1801-1807.
4. M.M. Al-Sawalha, M.S. Noorani. Application of the differential transformation method for the solution of the hyperchaotic Rossler system. Commun. Nonlinear Sci. Numer. Simul., 2009, 14: 1509-1514.
5. K. Hemida, M. Saad. Analytic approximations for fractional-order predator-Prey and rabies models. Journal of Advanced Research in Applied Mathematics, 2009, 1(1): 53-61.
6. K. Hemida, M. Saad. Application of the homotopy analysis method to fractional order gas dynamics equation. Journal of Advanced Research in Applied Mathematics, 2010, 2(1): 39-45, doi: 10.5373/jaram.264.102909.
7. K. Hemida, M. Saad. Numerical simulation of the generalized Huxley equation by homotopy analysis method. Journal of Applied Functional Analysis, 2010, 5(4): 344-350.
8. D. Hongmin, Li Tao, W. Qionghua, Li Hongbin. A fractional-order hyperchaotic system and its synchronization. Chaos, Solitons & Fractals, 2009, 41: 962-969.
9. S.J. Liao. The proposed homotopy analysis technique for the solution of nonlinear problem. Ph. D thesis, Shanghai Jiao Tong University, 1992.
10. S.J. Liao. An approximate solution technique which does not depend upon small parameters: a special example. Int. J. Nonlinear Mech. 1995, 30: 371-380, doi: 10.1016/0020-7462(94)00054-E.
11. S.J. Liao. An approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics. Int. J. Nonlinear Mech., 1997,32: 815-822, doi: 10.1016/S0020-7462(96)00101-1.
12. S.J. Liao. An explicit, totally analytic approximation of Blasius viscous flow problems. Int. J. Nonlinear Mech., 1999, 34(4): 759-778, doi: 10.1016/S0020-7462(98)00056-0.
13. S.J. Liao. Beyond perturbation: introduction to the homotopy analysis method. CRC Press, Boca Raton: Chapman& Hall, 2003.
14. S.J. Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput., 2004, 147: 499-513. doi: 10.1016/S0096-3003(02)00790-7.
15. S.J. Liao. Notes on the homotopy analysis method: Some defintions and theorems. Commun. Nonlinear Sci. Numer. Simul., 2009, 14: 983-997, doi: 10.1016/j.cnsns.2008.04.013.
16. Y. Luchko, R. Gorenflo. The initial-value problem for some fractional differential equations with Caputo derivative. Preprint Series A08-98, Fachbereich Mathematik and Informatic, Freie Universitat, Berlin, 1998.
17. K.S. Miller, B. Ross. An introduction to the fractional and fractional differential equations. John Wiley and Sons, New York, 1993.
18. K.B. Oldham, J. Spanier. The fractional calculus. Academic press, New York 1974.
19. I. Podlubny. Fractional differential equations. Academic press, San Diego-Boston-New York-London-Tokyo-Toronto, 1999.
20. M. Saad. Application of homotopy analysis method to fractional order generalized Huxley equation. Accepted in: Journal of Applied Functional Analysis.
21. M. Saad. Analytic approximations for fractional-order Newton-Leipnik system. Journal of Advanced Research in Scientific Computing, 2011, 3(2): 56-89.