In this paper, the fractional order of a new chaotic system was studied and the minimum effective dimension for which the system remains chaotic was calculated. We have presented the chaos synchronization of two identical and nonidentical fractional orders of the new system by using active control. Furthermore, the Laplace transform and the Niemann–Trouvaille fractional integral operator were used for synchronizing two system.
ArenaPCaponettoR (2000) Nonlinear Noninteger Order Circuits and Systems: An Introduction, Singapore: World Scientific.
2.
BaleanuDDiethelmKScalasETrujilloJJ (2012a) Fractional Calculus Models and Numerical Methods, Singapore: World Scientific.
3.
BaleanuDMachado, TenreiroJALuoAlbertC (2012b) Fractional Dynamics and Control, New York: Springer.
4.
ButzerPWestphalU (2000) An introduction to fractional calculus. Applications of Fractional Calculus in Physics, Singapore: World Scientific, pp. 1–85.
5.
FaieghiMRDelavariHBaleanuD (2011) Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control. Journal of Vibration and Control18: 1366–1374.
6.
GaoXYuJ (2005) Synchronization of two coupled fractional-order chaotic oscillators. Chaos, Solitons and Fractals26: 141–145.
7.
GrigorenkoIGrigorenkoE (2003) Chaotic dynamics of the fractional Lorenz system. Physical Review Letters91: 34101–34101.
8.
GolmankhanehKA (2012) Investigations in Dynamics: With Focus on Fractional Dynamics, Saarbruchen: Lap Lambert Academic Publishing.
9.
HartleyTTLorenzoCFKillory QammerH (1995) Chaos in a fractional order Chua’s system. Circuits and Systems I: IEEE Transactions on Fundamental Theory and Applications42: 485–490.
10.
HilferR (2000) Applications of Fractional Calculus in Physics, Singapore: World Scientific.
11.
LiCChenG (2004a) Chaos and hyperchaos in the fractional-order Rossler equations. Physica A: Statistical Mechanics and Its Applications341: 55–61.
12.
LiCChenG (2004b) Chaos in the fractional order Chen system and its control. Chaos, Solitons and Fractals22: 549–554.
13.
LiCYanJ (2007) The synchronization of three fractional differential systems. Chaos, Solitons and Fractals32: 751–757.
14.
LiCPDengWHXuD (2006) Chaos synchronization of the Chua system with a fractional order. Physica A: Statistical Mechanics and Its Applications360: 171–185.
15.
LiuCLingLTaoL (2009) A novel three dimensional autonomous chaos system. Chaos, Solitons and Fractals39: 1950–1958.
16.
LuJG (2006) Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal. Chaos, Solitons and Fractals27: 519–525.
17.
MatoukAE (2010) Dynamical behaviors, linear feedback control and synchronization of the fractional order Liu system. Journal of Nonlinear Systems and Applications3: 135–140.
18.
OdibatZM (2010) Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dynamics60: 479–487.
19.
PengG (2007) Synchronization of fractional order chaotic systems. Physics Letters A363: 426–432.
20.
PodlubnyI (1999) Fractional Differential Equations, San Diego, CA: Academic Press.
21.
SheuLJChenHKChenJHTamLMChenWCLinKT (2008) Chaos in the Newton–Leipnik system with fractional order. Chaos, Solitons and Fractals36: 98–103.
22.
SheuLJChenHKChenJHTamLM (2007) Chaos in a new system with fractional order. Chaos, Solitons and Fractals31: 1203–1212.
23.
SmakoSGKilbasAAMarichevO (1993) Fractional Integrals and Derivatives, Theory and Applications, Yverdon: Gordon and Breach.
24.
WangJXiongXZhangY (2006) Extending synchronization scheme to chaotic fractional-order Chen systems. Physica A: Statistical Mechanics and Its Applications370: 279–285.
25.
WuXLiJChenG (2008) Chaos in the fractional order unified system and its synchronization. Journal of the Franklin Institute345: 392–401.
26.
YanJLiC (2007) On chaos synchronization of fractional differential equations. Chaos, Solitons and Fractals32: 725–735.
27.
YuYLiH-X (2008) The synchronization of fractional-order Rossler hyperchaotic systems. Physica A: Statistical Mechanics and Its Applications387: 1393–1403.
28.
ZaslavskyGM (2005) Hamiltonian Chaos and Fractional Dynamics, New York: Oxford University Press.
29.
ZhouSLiHZhengzhouZ (2008) Chaos control and synchronization in a fractional neuron network system. Chaos, Solitons and Fractals36: 973–984.
30.
ZhouTLiC (2005) Synchronization in fractional-order differential systems. Physica D212: 111–125.
31.
ZhuHZhouSHeZ (2009) Chaos synchronization of the fractional-order Chen’s system. Chaos, Solitons and Fractals41: 2733–2740.
