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Journal articles on the topic 'Fractional Order'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Machado, J. A. Tenreiro. "Fractional order modelling of fractional-order holds." Nonlinear Dynamics 70, no. 1 (2012): 789–96. http://dx.doi.org/10.1007/s11071-012-0495-y.

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2

Soltan, A., A. G. Radwan, and Ahmed M. Soliman. "Fractional order filter with two fractional elements of dependant orders." Microelectronics Journal 43, no. 11 (2012): 818–27. http://dx.doi.org/10.1016/j.mejo.2012.06.009.

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3

Uddin, Md Jasim, S. M. Sohel Rana, and Md Motaleb Hossain. "COMPLEXITY ANALYSIS TO FRACTIONAL ORDER ENZYME MODEL." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (2023): 3178–85. http://dx.doi.org/10.47191/ijmcr/v11i1.09.

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This study examines a discrete-time enzyme model with Caputo fractional order. We look into the existence and uniqueness of fixed points in the discrete dynamic model and discover parametric criteria for their local asymptotic stability. Additionally, it is demonstrated using bifurcation theory that the system experiences Period-Doubling and Neimark-Sacker bifurcation in a constrained area around the singular positive fixed point and that an invariant circle would result. It has been determined that the parameter values and the initial conditions have a significant impact on the dynamical beha

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4

Mihaly, Vlad, Mircea Şuşcă, Eva H. Dulf, Dora Morar, and Petru Dobra. "Fractional Order Robust Controller for Fractional-Order Interval Plants." IFAC-PapersOnLine 55, no. 25 (2022): 151–56. http://dx.doi.org/10.1016/j.ifacol.2022.09.339.

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5

Tiwari, Bhupendra Nath, Dimple Singh Thakran, Priyanka Sejwal, Antim Vats, and Santosh Yadav. "Fractional order solutions to fractional order partial differential equations." SeMA Journal 77, no. 1 (2019): 27–46. http://dx.doi.org/10.1007/s40324-019-00200-2.

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6

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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7

Sengar, Kanchan, and Arun Kumar. "Fractional Order Capacitor in First-Order and Second-Order Filter." Micro and Nanosystems 12, no. 1 (2020): 75–78. http://dx.doi.org/10.2174/1876402911666190821100400.

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Background: Fractional order Butterworth and Chebyshev (low-pass filter circuits, highpass filter circuits and band-pass filters circuits) types of first and second order filter circuits have been simulated and their transfer function are derived. The effect of change of the fractional order α on the behavior of the circuits is investigated. Objective: This paper presents the use of fractional order capacitor in active filters. The expressions for the magnitude, phase, the quality factor, the right-phase frequencies, and the half power frequencies are derived and compared with their previous c

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8

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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9

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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10

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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11

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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12

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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13

Zhang, Qi, Baoye Song, Huadong Zhao, and Jiansheng Zhang. "Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders." Intelligent Control and Automation 08, no. 02 (2017): 75–85. http://dx.doi.org/10.4236/ica.2017.82006.

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14

Li, Wai-Kee. "Fractional bond order." Journal of Chemical Education 62, no. 7 (1985): 605. http://dx.doi.org/10.1021/ed062p605.

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15

Tenreiro Machado, J. A., Isabel S. Jesus, Alexandra Galhano, and J. Boaventura Cunha. "Fractional order electromagnetics." Signal Processing 86, no. 10 (2006): 2637–44. http://dx.doi.org/10.1016/j.sigpro.2006.02.010.

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16

Machado, J. Tenreiro. "Fractional order junctions." Communications in Nonlinear Science and Numerical Simulation 20, no. 1 (2015): 1–8. http://dx.doi.org/10.1016/j.cnsns.2014.05.006.

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17

Danca, Marius-F., and Jagan Mohan Jonnalagadda. "Fractional Order Curves." Symmetry 17, no. 3 (2025): 455. https://doi.org/10.3390/sym17030455.

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This paper continues the subject of symmetry breaking of fractional-order maps, previously addressed by one of the authors. Several known planar classes of curves of integer order are considered and transformed into their fractional order. Several known planar classes of curves of integer order are considered and transformed into their fractional order. For this purpose, the Grunwald–Letnikov numerical scheme is used. It is shown numerically that the aesthetic appeal of most of the considered curves of integer order is broken when the curves are transformed into fractional-order variants. The

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18

Idiou, Daoud, Abdelfatah Charef, and Abdelbaki Djouambi. "Linear fractional order system identification using adjustable fractional order differentiator." IET Signal Processing 8, no. 4 (2014): 398–409. http://dx.doi.org/10.1049/iet-spr.2013.0002.

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19

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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20

Kazem, S., S. Abbasbandy, and Sunil Kumar. "Fractional-order Legendre functions for solving fractional-order differential equations." Applied Mathematical Modelling 37, no. 7 (2013): 5498–510. http://dx.doi.org/10.1016/j.apm.2012.10.026.

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21

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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22

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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23

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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24

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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25

Wang, Yan, Ling Liu, Chongxin Liu, Ziwei Zhu, and Zhenquan Sun. "Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System." Mathematical Problems in Engineering 2018 (November 7, 2018): 1–10. http://dx.doi.org/10.1155/2018/8091757.

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In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance. Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated. And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters. The virtual control laws and pa

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26

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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27

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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28

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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29

Takeshita, Akihiro, Tomohiro Yamashita, Natsuki Kawaguchi, and Masaharu Kuroda. "Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System." Applied Sciences 11, no. 7 (2021): 3252. http://dx.doi.org/10.3390/app11073252.

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The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order

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30

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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31

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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32

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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33

Yoo, JinWoo. "An Affine Projection Algorithm with Pseudo-Fractional Projection Order." Transactions of The Korean Institute of Electrical Engineers 68, no. 7 (2019): 904–7. http://dx.doi.org/10.5370/kiee.2019.68.7.904.

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34

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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35

Valerii, Tytiuk, Chornyi Oleksii, Baranovskaya Mila та ін. "SYNTHESIS OF A FRACTIONAL-ORDER PIΛDΜ-CONTROLLER FOR A CLOSED SYSTEM OF SWITCHED RELUCTANCE MOTOR CONTROL". Eastern-European Journal of Enterprise Technologies 2, № 2 (98) (2019): 35–42. https://doi.org/10.15587/1729-4061.2019.160946.

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The relevance of creating high-quality control systems for electric drives with a switched reluctance motor (SRM) was substantiated. Using methods of mathematical modeling, transient characteristics of the process of turn-on of SRMs with various moments of inertia were obtained. Based on analysis of the obtained transient characteristics, features of the SRM turn-on process determined by dynamic change of parameters of the SRM during its turn-on were shown. Low accuracy of SRM identification using a fractionally rational function of rat34 class was shown. Regression coefficient of the resultin

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36

Leng, Bo Yang, Zhi Dong Qi, Liang Shan, and Hui Juan Bian. "Review of Fractional Order Control." Advanced Materials Research 1049-1050 (October 2014): 983–86. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.983.

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With the development of mathematical theory of fractional order, fractional order control system is more widely studied and discussed. In order to make the theory system of fractional order control systems perfect,this paper give out the review of fractional order control systems.The fractional order controller is divided into five categories to be described.

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37

Freeborn, Todd J., Brent Maundy та Ahmed Elwakil. "Fractional Resonance-BasedRLβCαFilters". Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/726721.

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We propose the use of a fractional order capacitor and fractional order inductor with orders0≤α, β≤1, respectively, in a fractionalRLβCαseries circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of(α+β)=1.1, 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the im

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38

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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39

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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40

Tarasov, Vasily E. "Fractional Probability Theory of Arbitrary Order." Fractal and Fractional 7, no. 2 (2023): 137. http://dx.doi.org/10.3390/fractalfract7020137.

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A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability density function (fractional PDF) is proposed. The basic properties of the fractional PDF are proven. The definition of the fractional cumulative distribution function (fractional CDF) is also suggested, and the basic properties of these functions are also proven. It is proven that the proposed fractional cumulative distribution functions gene

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41

Zhou, Ping, and Rui Ding. "Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative." Mathematical Problems in Engineering 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/214169.

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The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

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42

Kashkari, Bothayna S. H., and Muhammed I. Syam. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order." Applied Mathematics and Computation 290 (November 2016): 281–91. http://dx.doi.org/10.1016/j.amc.2016.06.003.

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43

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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44

Angstmann, Christopher N., Austen M. Erickson, Bruce I. Henry, Anna V. McGann, John M. Murray, and James A. Nichols. "Fractional Order Compartment Models." SIAM Journal on Applied Mathematics 77, no. 2 (2017): 430–46. http://dx.doi.org/10.1137/16m1069249.

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45

Ozair, Muhammad, Umer Saeed, and Takasar Hussain. "Fractional order SEIRS model." Advanced Studies in Biology 6 (2014): 47–56. http://dx.doi.org/10.12988/asb.2014.4312.

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46

Chen, YangQuan. "UBIQUITOUS FRACTIONAL ORDER CONTROLS?" IFAC Proceedings Volumes 39, no. 11 (2006): 481–92. http://dx.doi.org/10.3182/20060719-3-pt-4902.00081.

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47

Mohan, J. Jagan, and G. V. S. R. Deekshitulu. "Fractional Order Difference Equations." International Journal of Differential Equations 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/780619.

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A difference equation is a relation between the differences of a function at one or more general values of the independent variable. These equations usually describe the evolution of certain phenomena over the course of time. The present paper deals with the existence and uniqueness of solutions of fractional difference equations.

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48

Pu, Yi-Fei, and Xiao Yuan. "Fracmemristor: Fractional-Order Memristor." IEEE Access 4 (2016): 1872–88. http://dx.doi.org/10.1109/access.2016.2557818.

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49

Tenreiro Machado, J. "Fractional order describing functions." Signal Processing 107 (February 2015): 389–94. http://dx.doi.org/10.1016/j.sigpro.2014.05.012.

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50

Chen, Guangrong, Sheng Guo, Bowen Hou, and Junzheng Wang. "Fractional Order Impedance Control." IEEE Access 8 (2020): 48904–16. http://dx.doi.org/10.1109/access.2020.2979919.

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