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Journal articles on the topic 'Fractional Order Systems'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ping, Zhou, Cheng Yuan-Ming, and Kuang Fei. "Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)." Chinese Physics B 19, no. 9 (2010): 090503. http://dx.doi.org/10.1088/1674-1056/19/9/090503.

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2

Ortigueira, Manuel D., Duarte Valério, and J. Tenreiro Machado. "Variable order fractional systems." Communications in Nonlinear Science and Numerical Simulation 71 (June 2019): 231–43. http://dx.doi.org/10.1016/j.cnsns.2018.12.003.

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3

Li, Tianzeng, Yu Wang, and Yong Yang. "Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers." Discrete Dynamics in Nature and Society 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/408972.

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In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can be applied to an arbitrary four-dimensional fractional hyperchaotic system. And we give the optimal value of control parameters to achieve synchronization of fractional hyperchaotic system. This approach is universal, simple, and theoretically rigorous. Numerical simulations of several fractional-order hyperchaotic systems demonstrate the universality and t

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4

Wang, Chenhui. "Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems." Advances in Mathematical Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/3545083.

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Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed met

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5

Luo, Ying, Yang Quan Chen, Chun Yang Wang, and You Guo Pi. "Tuning fractional order proportional integral controllers for fractional order systems." Journal of Process Control 20, no. 7 (2010): 823–31. http://dx.doi.org/10.1016/j.jprocont.2010.04.011.

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6

Li, Yan, YangQuan Chen, and Hyo-Sung Ahn. "Fractional-order iterative learning control for fractional-order linear systems." Asian Journal of Control 13, no. 1 (2010): 54–63. http://dx.doi.org/10.1002/asjc.253.

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7

Hu, Jian-Bing, and Ling-Dong Zhao. "Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders." Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/264136.

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We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectivene

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8

Vafaei, Vajiheh, Hossein Kheiri, and Aliasghar Jodayree Akbarfam. "‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎." Boletim da Sociedade Paranaense de Matemática 39, no. 5 (2021): 57–72. http://dx.doi.org/10.5269/bspm.41252.

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In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to ver

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9

N’Doye, Ibrahima, Mohamed Darouach, Holger Voos, and Michel Zasadzinski. "Design of unknown input fractional-order observers for fractional-order systems." International Journal of Applied Mathematics and Computer Science 23, no. 3 (2013): 491–500. http://dx.doi.org/10.2478/amcs-2013-0037.

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Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of

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10

Bohdan, Kopchak, Marushchak Yaroslav, and Kushnir Andrii. "DEVISING A PROCEDURE FOR THE SYNTHESIS OF ELECTROMECHANICAL SYSTEMS WITH CASCADE-ENABLED FRACTIONAL-ORDER CONTROLLERS AND THEIR STUDY." Eastern-European Journal of Enterprise Technologies 5, no. 2 (101) (2019): 65–71. https://doi.org/10.15587/1729-4061.2019.177320.

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An approach to the synthesis of automatic control circuits has been proposed, based on a fractional characteristic polynomial, which makes it possible to ensure the desired quality of a transition process under condition for implementing a certain structure of the fractional controller, which depends on the transfer function of a control object. The use of fractional desirable forms extends the range of possible settings of fractional-order controllers in the synthesis of circuits for electrical-mechanical systems, ensures better quality of transients compared to the full-order controllers, an

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11

Rivero, Margarita, Sergei V. Rogosin, José A. Tenreiro Machado, and Juan J. Trujillo. "Stability of Fractional Order Systems." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/356215.

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The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a syste

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12

Fayazi, Ali. "Synchronization of Chaotic Fractional-Order Systems via Fractional-Order Adaptive Controller." Applied Mechanics and Materials 109 (October 2011): 333–39. http://dx.doi.org/10.4028/www.scientific.net/amm.109.333.

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In this paper, an adaptive fractional-order controller has been designed for synchronization of chaotic fractional-order systems. This controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. PID coefficients are updated using the gradient method when a proper sliding surface is chosen. To illustrate the effectiveness and performance of the controller, the proposed controller implements on a pair of topologically inequivalent chaotic fractional-order systems. The Genesio-Tessi and Coullet systems. Performance of fractional-orde

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13

Miao, Yue, Zhe Gao, and Chuang Yang. "Adaptive Fractional-order Unscented Kalman Filters for Nonlinear Fractional-order Systems." International Journal of Control, Automation and Systems 20, no. 4 (2022): 1283–93. http://dx.doi.org/10.1007/s12555-021-0163-4.

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14

Kheirizad, Iraj, Ali Akbar Jalali, and Khosro Khandani. "Stabilization of fractional-order unstable delay systems by fractional-order controllers." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226, no. 9 (2012): 1166–73. http://dx.doi.org/10.1177/0959651812453668.

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15

Martínez-Guerra, Rafael, and Lorenz Oliva Gonzalez. "Fractional order PI observer for a class of fractional order systems." Memorias del Congreso Nacional de Control Automático 6, no. 1 (2023): 497–502. http://dx.doi.org/10.58571/cnca.amca.2023.066.

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Currently the study of fractional order systems has become of great research interest, in particular the state estimation stands out within the lines of studies for this type of systems. Different methodologies have been proposed in order to solve this problem, however most of the techniques involve complete information of the system. Thus, this work presents a methodology for state estimation in a class of fractional order systems based on a fractional order observer which is constructed through an algebraic technique. This observer presents some significant properties, for instance, only var

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16

Zhao, Chunna, Murong Jiang, and Yaqun Huang. "Formal Verification of Fractional-Order PID Control Systems Using Higher-Order Logic." Fractal and Fractional 6, no. 9 (2022): 485. http://dx.doi.org/10.3390/fractalfract6090485.

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Fractional-order PID control is a landmark in the development of fractional-order control theory. It can improve the control precision and accuracy of systems and achieve more robust control results. As a theorem-proving formal verification method, it can be applied to an arbitrary system represented by a mathematical model. It is the ideal verification method because it is not subject to limits on state numbers. This paper presents the higher-order logic (HOL) formal verification and modeling of fractional-order PID controller systems. Firstly, a fractional-order PID controller was designed.

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17

Ma, Yancheng, Guoan Wu, and Lan Jiang. "Generalized Function Projective Lag Synchronization in Fractional-Order Chaotic Systems." International Journal of Information and Electronics Engineering 6, no. 5 (2016): 299–303. http://dx.doi.org/10.18178/ijiee.2016.6.5.642.

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18

Choudhary, S.K. "Stability and Performance Analysis of Fractional Order Control Systems." WSEAS Transactions on Systems and Control 9, no. 1 (2014): 438–44. https://doi.org/10.5281/zenodo.2590916.

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Fractional order system model represents the plant more adequately than integer order model. Fractional order controller is naturally the suitable choice for these fractional-order models as well as it is widely used for integer order model also. The significance of fractional order control is that it is a generalization of classical control theory. Most of the works in fractional order control systems are in theoretical nature and controller design and implementation in practice are very small. In this paper, stability and performance analysis of fractional order control systems are briefly e

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19

Zhang, Dong, and Shou Liang Yang. "Control Fractional-Order Continuous Chaotic System via a Simple Fractional-Order Controller." Applied Mechanics and Materials 336-338 (July 2013): 770–73. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.770.

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A universal fractional-order controller is proposed to asymptotically stable the unstable equilibrium points and the nonequilibrium points of continuous fractional-order chaos systems. The simple fractional-order controller is obtained based on the stability theorem of nonlinear fractional-order systems. The control scheme is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed fractional-order controller.

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20

Sun Ning. "Synchronization of fractional chaotic systems based on fractional-order interval systems." Acta Physica Sinica 60, no. 12 (2011): 120506. http://dx.doi.org/10.7498/aps.60.120506.

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21

Zhou, Ping, and Rui Ding. "Generalized Projective Synchronization for Fractional-Order Chaotic Systems with Different Fractional Order." Key Engineering Materials 474-476 (April 2011): 2106–9. http://dx.doi.org/10.4028/www.scientific.net/kem.474-476.2106.

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In this paper, we propose a generalized projective synchronization with different scaling factor for fractional-order chaotic systems with different fractional order. A method of constructing response system is given. The generalized projective synchronization conditions are obtained theoretically. Finally, the fractional-order Chen system is used to demonstrate the effectiveness of the proposed schemes.

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22

Nitisha, Shrivastava, and Baliyan Arjun. "Analysis of fractional order systems using newton iteration-based approximation techniq." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 1 (2023): 116–24. https://doi.org/10.11591/ijece.v13i1.pp116-124.

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Fractional differential equations play a major role in expressing mathematically the real-world problems as they help attain good fit to the experimental data. It is also known that fractional order controllers are more flexible than integer order controllers. But when it comes to the numerical approximation of fractional order functions inaccuracies arise if the conversion technique is not chosen properly. So, when a fractional order plant model is approximated to an integer order system, it is required that the approximated model be accurate, as the overall system performance is based on the

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23

Zhou, Ping, and Rongji Bai. "One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order1." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/490364.

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Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in1<q<2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order1<q<2is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

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24

Zhou, Mingcong, and Zhaoyan Wu. "Structure Identification of Fractional-Order Dynamical Network with Different Orders." Mathematics 9, no. 17 (2021): 2096. http://dx.doi.org/10.3390/math9172096.

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Topology structure and system parameters have a great influence on the dynamical behavior of dynamical networks. However, they are sometimes unknown or uncertain in advance. How to effectively identify them has been investigated in various network models, from integer-order networks to fractional-order networks with the same order. In the real world, many systems consist of subsystems with different fractional orders. Therefore, the structure identification of a dynamical network with different fractional orders is investigated in this paper. Through designing proper adaptive controllers and p

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25

Bouridah, Mohammed Salah, Toufik Bouden, and Müştak Erhan Yalçin. "Chaos Synchronization of Fractional-Order Lur’e Systems." International Journal of Bifurcation and Chaos 30, no. 14 (2020): 2050206. http://dx.doi.org/10.1142/s0218127420502065.

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Based on some essential concepts of fractional calculus and the theorem related to the fractional extension of Lyapunov direct method, we present in this paper a synchronization scheme of fractional-order Lur’e systems. A quadratic Lyapunov function is chosen to derive the synchronization criterion. The derived criterion is a suffcient condition for the asymptotic stability of the error system, formulated in the form of linear matrix inequality (LMI). The controller gain can be achieved by solving the LMI. The proposed scheme is illustrated for fractional-order Chua’s circuits and fractional-o

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26

Gao, Zhe, and Xiaozhong Liao. "Robust stability criterion of fractional-order functions for interval fractional-order systems." IET Control Theory & Applications 7, no. 1 (2013): 60–67. http://dx.doi.org/10.1049/iet-cta.2011.0356.

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27

Ramezani, Abdolrahman, and Behrouz Safarinejadian. "A Modified Fractional-Order Unscented Kalman Filter for Nonlinear Fractional-Order Systems." Circuits, Systems, and Signal Processing 37, no. 9 (2017): 3756–84. http://dx.doi.org/10.1007/s00034-017-0729-9.

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28

Luo, Ying, and YangQuan Chen. "Fractional order [proportional derivative] controller for a class of fractional order systems." Automatica 45, no. 10 (2009): 2446–50. http://dx.doi.org/10.1016/j.automatica.2009.06.022.

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29

Ivanescu, Mircea, Ioan Dumitrache, Nirvana Popescu, and Decebal Popescu. "Control Techniques for a Class of Fractional Order Systems." Mathematics 9, no. 19 (2021): 2357. http://dx.doi.org/10.3390/math9192357.

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The paper discusses several control techniques for a class of systems described by fractional order equations. The paper presents the unit frequency criteria that ensure the closed loop control for: Fractional Order Linear Systems, Fractional Order Linear Systems with nonlinear components, Time Delay Fractional Order Linear Systems, Time Delay Fractional Order Linear Systems with nonlinear components. The stability criterion is proposed for the systems composed of fractional order subsystems. These techniques are used in two applications: Soft Exoskeleton Glove Control, studied as a nonlinear

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30

Khanra, Munmun, Jayanta Pal, and Karabi Biswas. "Reduced Order Approximation of MIMO Fractional Order Systems." IEEE Journal on Emerging and Selected Topics in Circuits and Systems 3, no. 3 (2013): 451–58. http://dx.doi.org/10.1109/jetcas.2013.2265811.

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31

WANG, XING-YUAN, ZUN-WEN HU, and CHAO LUO. "GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS." International Journal of Modern Physics B 27, no. 30 (2013): 1350195. http://dx.doi.org/10.1142/s0217979213501956.

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In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the

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32

Qing, Wenjie, Binfeng Pan, Yueyang Hou, Shan Lu, and Wenjing Zhang. "Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems." Aerospace 9, no. 10 (2022): 616. http://dx.doi.org/10.3390/aerospace9100616.

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In this study, the problem of the stabilisation of a class of nonautonomous nonlinear systems was studied. First, a fractional stability theorem based on a fractional-order Lyapunov inequality was formulated. Then, a novel fractional-order sliding surface, which was a generalisation of integral, first-order, and second-order sliding surfaces with varying fractional orders, was proposed. Finally, a fractional-order sliding mode-based control for a class of nonlinear systems was designed. The stability property of the system with the proposed method was easily proven as a fractional Lyapunov dir

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33

Wang, Fei, and Yongqing Yang. "Correction: FRACTIONAL ORDER BARBALAT’S LEMMA AND ITS APPLICATIONS IN THE STABILITY OF FRACTIONAL ORDER NONLINEAR SYSTEMS." Mathematical Modelling and Analysis 22, no. 4 (2017): 503–13. http://dx.doi.org/10.3846/13926292.2017.1329755.

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This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first. Then, based on the relationship between Caputo fractional derivative and Riemann-Liouville fractional derivative, fractional order Barbalat’s lemma with Riemann-Liouville derivative is derived. Furthermore, according to these results, a set of new formulations of Lyapunov-like lemmas for fractional order nonlinear systems are established. Finally, an example is presented to verify the theoretical results in this paper

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34

WANG, XING-YUAN, GUO-BIN ZHAO, and YU-HONG YANG. "DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS." International Journal of Modern Physics B 27, no. 11 (2013): 1350034. http://dx.doi.org/10.1142/s0217979213500343.

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This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order

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35

Cao, Xiangyang, Leipo Liu, and Hao Xing. "Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems." International Journal of Innovative Research in Computer Science & Technology 5, no. 4 (2017): 333–38. http://dx.doi.org/10.21276/ijircst.2017.5.4.7.

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36

Bingi, Kishore, Rosdiazli Ibrahim, Mohd Noh Karsiti, Sabo Miya Hassan, and Vivekananda Rajah Harindran. "An Integer-Order Transfer Function Estimation Algorithm for Fractional-Order PID Controllers." International Journal of Applied Metaheuristic Computing 11, no. 3 (2020): 133–50. http://dx.doi.org/10.4018/ijamc.2020070108.

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Fractional-order systems and controllers have been extensively used in many control applications to achieve robust modeling and controlling performance. To implement these systems, curve fitting based integer-order transfer function estimation techniques namely Oustaloup and Matsuda are most widely used. However, these methods are failed to achieve the best approximation due to the limitation of the desired frequency range. Thus, this article presents a simple curve fitting based integer-order transfer function estimation method for fractional-order differentiator/integrator using frequency re

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37

Aguila-Camacho, N., J. Gallegos, and M. A. Duarte-Mermoud. "Analysis of fractional order error models in adaptive systems: Mixed order cases." Fractional Calculus and Applied Analysis 22, no. 4 (2019): 1113–32. http://dx.doi.org/10.1515/fca-2019-0058.

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Abstract This paper presents the properties of two fractional order error models (FOEM) that arise in the analysis of fractional order adaptive systems (FOAS). Cases where the fractional order is the same for every equation in these two FOEM were analyzed in a previous work, obtaining useful results. However, those cases where the fractional orders are different in the equations of FOEM (mixed order cases) have not been addressed before. This paper treats the analysis of some of these mixed order cases, proving boundedness of all the signals and convergence to zero of the mean value of the squ

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38

Wang, Zhen, Xia Huang, and Zhao Zhao. "Synchronization of nonidentical chaotic fractional-order systems with different orders of fractional derivatives." Nonlinear Dynamics 69, no. 3 (2012): 999–1007. http://dx.doi.org/10.1007/s11071-011-0322-x.

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39

Gao, Fei, Xue-Jing Lee, Heng-qing Tong, Feng-xia Fei, and Hua-ling Zhao. "Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/382834.

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In this paper, a non-Lyapunov novel approach is proposed to estimate the unknown parameters and orders together for noncommensurate and hyper fractional chaotic systems based on cuckoo search oriented statistically by the differential evolution (CSODE). Firstly, a novel Gaos’ mathematical model is proposed and analyzed in three submodels, not only for the unknown orders and parameters’ identification but also for systems’ reconstruction of fractional chaos systems with time delays or not. Then the problems of fractional-order chaos’ identification are converted into a multiple modal nonnegativ

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40

Sierociuk, Dominik, and Pawel Ziubinski. "Fractional Order Estimation Schemes for Fractional and Integer Order Systems with Constant and Variable Fractional Order Colored Noise." Circuits, Systems, and Signal Processing 33, no. 12 (2014): 3861–82. http://dx.doi.org/10.1007/s00034-014-9835-0.

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41

Saadaoui, Karim. "Stability Regions of Fractional First Order Controllers Applied to Fractional Order Delay Systems." International Journal of Mathematical Models and Methods in Applied Sciences 15 (April 22, 2021): 86–90. http://dx.doi.org/10.46300/9101.2021.15.12.

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This paper focuses on the problem of stabilizing fractional order time delay systems by fractional first order controllers. A solution is proposed to find the set of all stability regions in the controller’s parameter space. The D-decomposition method is employed to find the real root boundary and complex root boundaries which are used to identify the stability regions. Illustrative examples are given to show the effectiveness of the proposed approach, and it is remarked that the stability region obtained for the fractional order controller is larger than the non-fractional controller.

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42

Allogmany, Reem, Nada A. Almuallem, Reima Daher Alsemiry, and Mohamed A. Abdoon. "Exploring Chaos in Fractional Order Systems: A Study of Constant and Variable-Order Dynamics." Symmetry 17, no. 4 (2025): 605. https://doi.org/10.3390/sym17040605.

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Fractional calculus generalizes well-known differentiation and integration to noninteger orders, allowing a more accurate framework for modeling complex dynamical behaviors. The application of fractional-order systems is quite wide in engineering, biology, and physics because they inherently capture the memory effects and long-range dependencies. Out of these, fractional jerk chaotic systems have gained attention regarding their applications in secure communication, signal processing, and control systems. This work develops a comparative analysis of a fractional jerk system that includes const

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43

Guel‐Cortez, Adrian‐Josue, César‐Fernando Méndez‐Barrios, Eun‐jin Kim, and Mihir Sen. "Fractional‐order controllers for irrational systems." IET Control Theory & Applications 15, no. 7 (2021): 965–77. http://dx.doi.org/10.1049/cth2.12095.

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44

Lopes, António M., and Liping Chen. "Fractional Order Systems and Their Applications." Fractal and Fractional 6, no. 7 (2022): 389. http://dx.doi.org/10.3390/fractalfract6070389.

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45

Adams, Jay L., and Tom t. Hartley. "Hankel operators for fractional-order systems." Journal Européen des Systèmes Automatisés 42, no. 6-8 (2008): 701–13. http://dx.doi.org/10.3166/jesa.42.701-713.

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46

Zhou, Tianshou, and Changpin Li. "Synchronization in fractional-order differential systems." Physica D: Nonlinear Phenomena 212, no. 1-2 (2005): 111–25. http://dx.doi.org/10.1016/j.physd.2005.09.012.

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47

Peng, Guojun. "Synchronization of fractional order chaotic systems." Physics Letters A 363, no. 5-6 (2007): 426–32. http://dx.doi.org/10.1016/j.physleta.2006.11.053.

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HosseinNia, S. Hassan, Inés Tejado, and Blas M. Vinagre. "Stability of fractional order switching systems." Computers & Mathematics with Applications 66, no. 5 (2013): 585–96. http://dx.doi.org/10.1016/j.camwa.2013.05.005.

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Ahmad, Wajdi M. "Hyperchaos in fractional order nonlinear systems." Chaos, Solitons & Fractals 26, no. 5 (2005): 1459–65. http://dx.doi.org/10.1016/j.chaos.2005.03.031.

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Wu, Zeng-bao, and Yun-zhi Zou. "Global fractional-order projective dynamical systems." Communications in Nonlinear Science and Numerical Simulation 19, no. 8 (2014): 2811–19. http://dx.doi.org/10.1016/j.cnsns.2014.01.007.

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