Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier, 2006
|
Petras I. Fractional-order Nonlinear Systems: Modeling, Analysis and Simulation. Beijing: Higher Education Press, 2011
|
Rossikhin YA, Shitikova MV. Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results. Applied Mechanics Reviews, 2010, 63: 010801-1-52
|
Machado JAT, Kiryakova V, Mainardi F. Recent history of fractional calculus. Communications in Nonlinear Science and Numerical Simulation, 2011, 16: 1140-1153
|
Wang ZH, Hu HY. Stability of a linear oscillator with damping force of fractional order derivative. Science China: Physics, Mechanics & Astronomy, 2010, 53(2): 345-352
|
Wang ZH, Du ML. Asymptotical behavior of the solution of a SDOF linear fractionally damped vibration system. Shock and Vibration, 2011, 18: 257-268
|
Li GG, Zhu ZZ, Cheng CJ. Dynamical stability of viscoelastic column with fractional derivative constitutive relation. Applied Mathematics and Mechanics, 2001, 22 (3): 294-303
|
Deng WH, Li CP. The evolution of chaotic dynamics for fractional unified system. Physics Letters A, 2008, 372(4): 401-407
|
Cao JY, Ma CB, Xie H, et al. Nonlinear dynamics of Duffing system with fractional order damping. ASME Journal of Computational and Nonlinear Dynamics, 2010, 5: 041012-1-6
|
Wu XJ, Lu HT, Shen SL. Synchronization of a new fractional-order hyperchaotic system. Physics Letters A, 2009, 373: 2329-2337
|
Lu JG. Chaotic dynamics of the fractional-order Lü system and its synchronization. Physics Letters A, 2006, 354: 305-311
|
Wahi P, Chatterjee A. Averaging oscillations with small fractional damping and delayed terms. Nonlinear Dynamics, 2004, 38: 3-22
|
Li CP, Deng WH, Remarks on fractional derivatives. Applied Mathematics and Computation, 2007, 187(2): 777-784
|
陈林聪,朱位秋,谐和与宽带噪声联合激励下含分数导数型阻尼的Duffing振子的平稳响应. 应用力学学报,2010,27(3):517-521 (Chen Lincong, Zhu Weiqiu. Stationary response of duffing oscillator with fractional derivative damping under combined harmonic and wide band noise xcitations. Chinese Journal of Applied Mechanics, 2010,27(3):517-521 (in Chinese)
|
李媛萍, 张卫. 分数阶ver del Pol-Duffing系统的非线性动力学行为分析. 振动与冲击,2011,30(7):164-168 (Li Yuanping, Zhang Wei. Nonlinear dynamic behavior of a fractional-order ver del pol-duffing system. Journal of Vibration and Shock, 2011, 30(7): 164-168 (in Chinese)
|
申永军,杨绍普,邢海军. 含分数阶微分的线性单自由度振子的动力学分析. 物理学报,2012,61(11): 110505-1-6 (Shen Yongjun, Yang Shaoping, Xing Haijun. Dynamical analysis of linear single degree-of-freedom oscillator with fractional-order derivative. Acta Physica Sinica, 2012, 61(11): 110505-1-6 (in Chinese)
|
Shen YJ, Yang SP, Xing HJ, et al. Primary resonance of Duffing oscillator with fractional-order derivative. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(7): 3092-3100
|