[1] Zaslavsky G M. Chaos, fractional kinetics and anomalous transport. Phys Rep, 2002, 371(6): 461–580

[2] Tarasov V E, Zaslavsky G M. Dynamics with low-level fractionality. Physica A, 2006, 368(2): 399–415

[3] Riewe F. Mechanics with fractional derivatives. Phys Rev E, 1997, 55(3): 3581–3592

[4] Tarasov V E. Fractional systems and fractional Bogoliubov hierarchy equations. Phys Rev E, 2005, 71(1): 011102

[5] Tarasov V E. Fractional Liouville and BBGKI equations. J Phys Conf Ser, 2005, 7: 17–33

[6] Nigmatullin R. The realization of the generalized transfer in a medium with fractal geometry. Phys Status Solidi B, 1986, 133(1): 425–430

[7] Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable func-tions further results. Comput Math Appl, 2006, 51(9/10): 1367–1376

[8] Jumarie G. Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions. Appl Math Lett, 2009, 22(3): 378–385

[9] Sachin Bhalekar, Varsha Daftardar-Gejji. Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simulat, 2010, 15(11): 3536–3546

[10] Zhang S Q. Existence of solution for a boundary value problem of fractional order. Acta Math Sci, 2006, 26B(2): 220–228

[11] Metzler R, Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J Phys A, 2004, 37(31): 161–208

[12] Klimek M. Sequential fractional differential equations with Hadamard derivative. Commun Nonlinear Sci Numer Simulat, 2011, 16(12): 4689–4697

[13] Yu F J, Zhang H Q. Fractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy. Int J Theor Phys, 2007, 46(12): 3182–3192

[14] Yu F J, Zhang H Q. A new fractional order soliton equation hierarchy and its integrable coupling system. Appl Math Comput, 2007, 194(1): 259–266

[15] Yu F J, Zhang H Q. New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy. Chaos, Solitons and Fractals, 2008, 37(3): 688–697

[16] Yu F J. A generalized fractional KN equation hierarchy and its fractional Hamiltonian structure. Comput Math Appl, 2011, 62(3): 1522–1530

[17] Tu G Z. The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. J Math Phys, 1989, 30(2): 330–338

[18] Ma W X. A new Liouville integrable generalized Hamiltonian equations and its reduction. Chinese J Contemp Math, 1992, 13(1): 79–89

[19] Zhang Y F. A generalized multi-component AKNS hierarchy. Phys Lett A, 2004, 327(5/6): 438-441

[20] Zhang Y F, Tam H. Application of two loop algebras. Chaos, Solitons and Fractals, 2007, 32(2): 640–644

[21] Tao S X, Xia T C. The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure. Chin Phys B, 2010, 19: 070202

[22] Zhang Y F, Fan E G. An approach for generating enlarging integrable systems. Phys Lett A, 365(1/2): 89–96

[23] Wu G C, Zhang S. A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy. Phys Lett A, 2011, 375(42): 3659–3663

[24] Ma W X, Fuchssteiner B, Integrable theory of the perturbation equations. Chaos, Solitons and Fractals, 1996, 7(8): 1227–1250

[25] Ma W X. Integrable couplings of vector AKNS soliton equations. J Math Phys, 2005, 46(3): 033507

[26] Zhang Y F, Zhang H Q. A direct method for integrable couplings of TD hierarchy. J Math Phys, 2002, 43(1): 466–472

[27] Ma W X. A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order. Phys Lett A, 2007, 367(6): 473–477

[28] Xia T C, Zhang D P. New integrable couplings of Tu hierarchy with self-consistent sources. Acta Math Sci, 2012, 32A(5): 941–949

[29] Zhang Y F. A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system. Chaos, Solitons and Fractals, 2004, 21(2): 305–310

[30] Xia T C. Two new integrable couplings of the soliton hierarchies with self-consistent sources. Chin Phys B, 2010, 19: 100303

[31] Zhang Y F. Lie algebras for constructing nonlinear integrable couplings. Commun Theor Phys, 2011, 56(5): 805–812

[32] Zhang J, You F C. Generalized trace variational identity and its applications to fractional integrable couplings. Commun Frac Calc, 2011, 2(2): 36–44

[33] Tu G Z. On Liouville integrability of zero-curvature equations and the Yang hierarchy. J Phys A: Math Gen, 1989, 22(13): 2375–2392