References
[1] Ott, E., Grebogi, C. and Yorke, J.A. (1990). Controlling chaos. Physical Review Letters, American Physical Society. 64, 1196–9. https://doi.org/10.1103.64.1196.
[2] Pyragas, K. (1992). Continuous control of chaos by self-controlling feedback. Physics Letters A, 170, 421–8.
https://doi.org/10.1016/0375-9601(92)90745-8.
[3] Socolar, J.E.S., Sukow, D.W. and Gauthier, D.J. (1994). Stabilizing unstable periodic orbits in fast dynamical systems. Physical Review E, American Physical Society. 50, 3245–8. https://doi.org/10.1103/PhysRevE.50.3245.
[4] Pyragas, V. and Pyragas, K. (2011). Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay. Physics Letters A, 375, 3866–71. https://doi.org/10.1016/j.physleta.2011.08.072.
[5] Lehnert, J., Hövel, P., Flunkert, V., Guzenko, P.Yu., Fradkov, A.L., and Schöll, E. (2011). Adaptive tuning of feedback gain in time-delayed feedback control. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21, 043111.
https://doi.org/10.1063/1.3647320.
[6] Hilfer, R. (2000). Applications of Fractional Calculus In Physics. World Scientific.
[7] Xu, Z.-D., Xu, C., and Hu, J. (2015). Equivalent fractional Kelvin model and experimental study on viscoelastic damper. Journal of Vibration and Control, SAGE Publications Ltd STM. 21, 2536–52. https://doi.org/10.1177/1077546313513604.
[8] Rossikhin, Y.A. and Shitikova, M.V. (2009). Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results. Applied Mechanics Reviews, 63. https://doi.org/10.1115/1.4000563.
[9] Vinagre, B.M., Monje, C.A., Calderón, A.J., and Suárez, J.I. (2007). Fractional PID Controllers for Industry Application. A Brief Introduction. Journal of Vibration and Control, SAGE Publications Ltd STM. 13, 1419–29.
https://doi.org/10.1177/1077546307077498.
[10] Yin, C., Chen, Y., and Zhong, S. (2014). Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Automatica, 50, 3173–81. https://doi.org/10.1016/j.automatica.2014.10.027
[11] Sun, G., Wu, L., Kuang, Z., Ma, Z., and Liu, J. (2018). Practical tracking control of linear motor via fractional-order sliding mode. Auto-matica, 94, 221–35. https://doi.org/10.1016/j.automatica.2018.02.011.
[12] Dabiri, A., Moghaddam, B.P., and Machado, J.A.T. (2018). Optimal variable-order fractional PID controllers for dynamical systems. Journal of Computational and Applied Mathematics, 339, 40–8. https://doi.org/10.1016/j.cam.2018.02.029.
[13] El-Dessoky, M.M., and Khan, M.A. (2019). Application of fractional calculus to combined modified function projective synchronization of different systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29, 013107.
https://doi.org/10.1063/1.5079955.
[14] Tavazoei, M.S. and Haeri, M. (2008). Stabilization of Unstable Fixed Points of Chaotic Fractional Order Systems by a State Fractional PI Controller. European Journal of Control, 14, 247–57. https://doi.org/10.3166/ejc.14.247-257.
[15] Tavazoei, M.S. and Haeri, M. (2008). Chaos control via a simple fractional-order controller. Physics Letters A, 372, 798–807. https://doi.org/10.1016/j.physleta.2007.08.040.
[16] Soukkou, A., Boukabou, A. and Leulmi, S. (2016). Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems. Nonlinear Dynamics, 85, 2183–206. https://doi.org/10.1007/s11071-016-2823-0.
[17] Pahnehkolaei, S.M.A., Alfi, A., and Tenreiro Machado, J.A. (2017). Chaos suppression in fractional systems using adaptive fractional state feedback control. Chaos, Solitons & Fractals, 103, 488–503. https://doi.org/10.1016/j.chaos.2017.06.003.
[18] Sadeghian, H., Salarieh, H., Alasty, A., and Meghdari, A. (2011). On the control of chaos via fractional delayed feedback method. Computers & Mathematics with Applications, 62, 1482–91. https://doi.org/10.1016/j.camwa.2011.05.002.
[19] Soukkou, A., Boukabou, A., and Goutas, A. (2018). Generalized fractional-order time-delayed feedback control and synchronization designs for a class of fractional-order chaotic systems. International Journal of General Systems, Taylor & Francis. 47, 679–713. https://doi.org/10.1080/03081079.2018.1512601.
[20] Chen, M. and Han, Z. (2003). Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos, Solitons & Fractals, 17, 709–16. https://doi.org/10.1016/S0960-0779(02)00487-3.
[21] Liu, Q.X., Liu, J.K., and Chen, Y.M. (2016). An explicit hybrid method for multi-term fractional differential equations based on Adams and Runge-Kutta schemes. Nonlinear Dynamics, 84, 2195–203. https://doi.org/10.1007/s11071-016-2638-z.
[22] Gjurchinovski, A., Sandev, T., and Urumov, V. (2010). Delayed feedback control of fractional-order chaotic systems. Journal of Physics A: Mathematical and Theoretical, 43, 445102. https://doi.org/10.1088/1751-8113/43/44/445102.
[23] Minming H., Qin H., and Xi W. (2020). Dynamically adaptive cuckoo search algorithm based on dimension by opposition-based learning. Application Research of Computers, 37, 1015-9. https://doi.org/10.19734/j.issn.1001-3695.2018.10.0725.