[1] I. Podlubny, “Fractional differential equations,” Academic Press, New York (1999).
[2] K. Diethelm and J.F. Neville, “Analysis of fractional differential equations, ” Journal of Mathematical Analysis and Applications, vol 48, pp. 265-229 ,2002.
[3] C.A. Monje, Y. Chen, B.M. Vinagre, D. Xue, and V. Feliu-Batlle, “Fractional-order systems and controls,”fundamentals and applications. Springer, Berlin ,2010.
[4] Y. Guo, Z. Deng, L. Zu and Y. Lv, “Trajectory tracking control of a quad-rotor using fractional-order sliding mode, ” 2017 36th
Chinese Control Conference (CCC), Dalian, pp. 6414-6419, 2017.
[5] M. Dalir,“Applications of fractional calculus,” Appl. Math. Sci., vol 4, pp. 1021–32, 2010
[6] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo,“Theory and applications of fractional differential equations,” Elsevier, 2006.
[7] A. Ebaid,“Analysis of projectile motion in view of fractional calculus, ” Appl. Math. Model, vol 35,pp.1231–9, 2011.
[8] AbouOmar, M.S.; Zhang, H.J.; Su, Y.X. Fractional Order Fuzzy PID Control of Automotive PEM Fuel Cell Air Feed System Using Neural Network Optimization Algorithm. Energies , vol 12, 2019.
[9] J.D. Gabano , and T. Poinot,“Fractional modelling and identification of thermal Systems, ” Sig Process 2011;vol 91, pp. 531–41, 2011.
[10] R.L. Magin,“Fractional calculus in bioengineering, ” Crit. Rev. Biomed. Eng., vol 32,pp. 1–104, 2004.
[11] M.S. Couceiro, N.M.F. Ferreira, and J.A. Machado,“Application of fractional algorithms in the control of a robotic bird,” Commun. Nonlin. Sci. Numer Simul. vol 15 pp. 895–910,2010.
[12] A. Tepljakov, E. Petlenkov, and J. Belikov,“Fopid controller tuning for fractional fopdt plants subject to design specifications in the frequency domain, ”. European control conference.IEEE. 2015.
[13] Z.M. Odibat,“Adaptive feedback control and synchronization of non-identical chaotic fractional order systems,” Nonlinear Dyn. vol 60, pp. 479–87, 2009.
[14] Agrawal,“A general formulation and solution scheme for fractional optimal control problems,” Nonlinear Dyn., vol 38, pp. 323–37, 2004.
[15] Y. Li , S. Tong , L. Liu , and G. Feng ,“Adaptive output-feedback control design with prescribed performance for switched nonlinear systems, ”, Automatica 80, pp. 225–231, 2017 .
[16] Y. Li , S. Tong , Y. Liu , T. Li,“Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on small-gain approach,” IEEE Trans. Fuzzy Syst. vol 22, pp. 164–176,2014
[17] W. Perruquetti, and J.P. Barbot,“Sliding mode control in engineering , ” New York: Marcel Dekker; 2002.
[18] S.Pashaei, M. Badamchizadeh,“ A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances,”ISA Transactions63,pp. 39–48,2016.
[19] E.P. Wilfrid, and J.P. Barbot ,“Sliding mode control in engineering, ” Marcel dekker INC., 2002.
[20] H.C. Han,“Lmi-based sliding surface design for integral sliding mode control of mismatched uncertain systems, ” IEEE Trans Autom Control, vol 52, pp. 736–42, 2007.
[21] K.S. Kim, Y. Park, and S.H. Oh,“Designing robust sliding hyperplanes for parametric uncertain systems: a riccati approach, Automatica , vol 36, pp.1041–8,2000.
[22] V.I. Utkin, and A.S. Poznyak ,“Adaptive sliding mode control, ” vol. 440, Lecture Notes in Control & Information Sciences; 2013.
[23] S.W.Wang, D.W. Yu, and D.L. Yu,“Compensation for unmatched uncertainty with adaptive rbf network, ” Int. J. Eng. Sci. vol 3, pp. 801–4, 2011.
[24] Z. Gao, and X. Liao,“Integral sliding mode control for fractional-order systems with mismatched uncertainties, ”Nonlinear Dyn., vol 72, pp. 27–35, 2013.
[25] D. Y. Chen, X.X. Liu, X.Y. Ma, and R.F. Zhang, “Control of a class of fractional-order chaotic systems via sliding mode, ” Nonlinear Dyn., vol 67, pp. 893–901, 2011.
[26] K. Mathiyalagan, G. Sangeetha, “Second-order sliding mode control for nonlinear fractional-order systems, ” Appl. Math. Comput., vol 383, 2020.
[27] Y. Chen, Y. Wei, H. Zhong, and Y. Wang,“Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems, ” Nonlinear Dyn., pp. 1–11, 2016.
[28] M.P. Aghababa,“ Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller,”Commun. Nonlinear Sci. Numer. Simulat, vol 17, pp.2670–81, 2012.
[29] M.P. Aghababa,“Synchronization and stabilization of fractional second-order nonlinear complex system, ” Nonlinear Dyn., pp. 1–14, 2014.
[30] M.P. Aghababa,“A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems, ” Nonlinear Dyn,. vol 73, pp. 679–88, 2013.
[31] T. Binazadeh, and M.H. Shafiei,“Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach, ” Mechatronics, vol 23, pp. 888-892, 2013.
[32] A. Pisano, M.R. Rapaic, Z.D. Jelicic, and E. Usai,“ Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics,” Int J Robust Nonlin., vol 20, pp. 2045–56, 2010.
[33] S. Dadras, and H.R. Momeni, Control of a fractional-order economical system via sliding mode, ” Physica A, vol 389, pp. 2434–42, 2010.
[34] B. Zhang, Y. Pi, and Y. Luo,“ Fractional order sliding mode control based on parameter auto-tuning for velocity control of permanent magnet synchronous motor, ” ISA Trans. 2, vol 51, pp. 649–56, 2012.
[35] A. Razminia, and D. Baleanu,“Complete synchronization of commensurate fractional order chaotic systems using sliding mode control, ” Mechatronics, vol 23,pp. 873–9, 2013.
[36] Y. Tang, X. Zhang, D. Zhang, G. Zhao, and X. Guan,“ Fractional order sliding mode controller design for antilock braking systems, ” Neurocomputing, vol 111,pp..122–30, 2013.
[37] I. Podlubny,“ Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, ” Academic press; 1999. p.198.
[38] V. Duarte, and S. Jose ,“An Introduction to Fractional Control, ” IET CONTROL ENGINEERING SERIES 91
[39] A. RHIF, Z. Kardous, and B.B. Naceur ,“A PID-Sliding Mode Control Design for a Coupled Tank, ” International Conference CRATT’2012, Rades, Tunisia 2012.
[40] A.Rhif, “A Sliding Mode Control with a PID sliding surface for Poweroutput Maximizing of a Wind Turbine,” STM, Journal of Instrumentation and Control, vol.1, pp. 11-16, 2012
[41] G. Chen, “Conventional and Fuzzy PID Controllers: An Overview”, Int. J. Intell. Control Syst., vol. 1, pp. 235-246, 1996.
[42] O. Shaheen, A.M. El-Nagar, M. El-Bardini, and N.M. El-Rabaie,“Probabilistic fuzzy logic controller for uncertain nonlinear systems, ” Journal of the Franklin Institute, vol 355, pp. 1088–1106, 2018.