In this paper, we use the fractional Laplace decomposition method (FLDM) to solve fractional chaotic systems that have various applications in engineering. The FLDM is simple to apply and, moreover, has advantages of manipulating the series solution in an efficient way. We have used the obtained series solutions to generate chaotic sequences.
AhmedNAMamatMKavikumarJ (2012) Solving fuzzy Duffing’s Equation by the Laplace transform decomposition. Applied Mathematical Sciences6(59): 2935–2944.
2.
AlomariAKNooraniMSMNazarR (2010) Homotopy analysis method for solving fractional Lorenz system. Communication in Nonlinear Science & Numerical Simulations15: 1864–1872.
3.
ArmanKBKiaFNaserP (2010) A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Communication in Nonlinear Science & Numerical Simulations15: 1864–1872.
4.
BuffoniB (1996) Periodic and homoclinic orbits for Lorenz-Lagrangian systems via variational methods. Nonlinear Analysis: Theory Methods & Applications26: 443–462.
5.
ElcinY (2006) Numerical solution of Duffing equation by the Laplace decomposition algorithm. Applied Mathematics & Computations177: 572–580.
6.
GondalMAKhanM (2010) Homotopy perturbation method for nonlinear exponential boundary layer equation using Laplace transformation, He’s polynomials and Pade technology He's polynomials and Pade technology. International Journal of Nonlinear Sciences and Numerical Simulation11: 1145–1153.
7.
GondalMAArifeASKhanMHussainI (2011) An efficient numerical method for solving linear and nonlinear partial differential equations by combining homotopy analysis and transform method. World Applied Sciences Journal14: 1786–1791.
8.
Gondal MA, Salah A, Khan M and Batool SI (2012) A novel analytical solution of a fractional diffusion problem by homotopy analysis transform method. Neural Computing and Applications, August 2012. DOI:10.1007/s00521-012-1120-1.
9.
HashimINooraniMSMAhmadR (2006) Accuracy of the Adomian decomposition method applied to the Lorenz system. Chaos Solitons & Fractals28: 1149–1158.
10.
HosseinzadehHJafariHRoohaniM (2010) Application of Laplace decomposition method for solving Klein-Gordon equation. World Applied Sciences Journal8: 809–813.
JianpingYChangpinLi (2007) On chaos synchronization of fractional differential equations. Chaos Solitons & Fractals32: 725–735.
13.
KhanMGondalMA (2010a) A new analytical solution of foam drainage equation by Laplace decomposition method. Journal of Advanced Research in Differential Equations2: 53–64.
14.
KhanMGondalMA (2010b) New modified Laplace decomposition algorithm for Blasius flow equation. Journal of Advanced Research in Scientific Computing2: 35–43.
15.
KhanMGondalMA (2011a) A new analytical approach to solve Thomas-Fermi equation. World Applied Sciences Journal12: 2309–2313.
16.
KhanMGondalMA (2011b) An efficient two step Laplace decomposition algorithm for singular Volterra integral equations. International Journal of Physical Science6(20): 4717–4720.
17.
KhanMGondalMA (2011c) Restrictions and Improvements of Laplace decomposition method. Journal of Advanced Research in Scientific Computing3: 8–14.
18.
KhanMGondalMA (2012a) A new analytical solution procedure for nonlinear integral equations. Mathematical and Computer Modelling55: 1892–1897.
19.
KhanMGondalMA (2012b) A reliable treatment of Abel’s second kind singular integral equations. Applied Mathematics Letters25: 1666–1670.
20.
Khan M, Gondal MA and Batool SI (2012a) A new modified Laplace decomposition method for higher order boundary value problems. Computational and Mathematical Organization Theory, July 2012. DOI: 10.1007/s10588-012-9123-0.
21.
KhanMGondalMAKumarS (2012b) A novel homotopy perturbation transform algorithm for linear and nonlinear system of partial differential equations. World Applied Sciences Journal12(12): 2352–2357.
22.
KhanMHussainM (2011) Application of Laplace decomposition method on semi-infinite domain. Numerical Algorithms56: 211–218.
23.
KiymazO (2009) An algorithm for solving initial value problems using Laplace Adomian decomposition method. Applied Mathematical Sciences3: 1453–1459.
24.
MerdanM (2009) Variational iteration and homotopy perturbation method for solving Lorenz system. BAÜFBE Dergisi11: 3–14.
25.
Salah A, Khan M and Gondal MA (2012) A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method. Neural Computing and Applications. February 2012. DOI: 10.1007/s00521-012-0855-z.