Recent developments on the realization of fractance device

References

[1] A. Chareff, H. H. Sun, Y. Y. Tsao, and B. Onaral, Fractal system as represented by singularity function. IEEE Trans. on Automatic Control 37, No 9 (1992), 1465–1470.10.1109/9.159595Search in Google Scholar

[2] A. Charef, Analogue realisation of fractional order integartor, differentiator and fractional PI^λD^μ controller. IEEE Proc. of Control Theory Applications 153, No 6 (2006), 714–720.10.1049/ip-cta:20050019Search in Google Scholar

[3] A. Khovanskii, The Application of Continued Fractions and Their generalizations to Problems in Approximation Theory. P. Noordhoff Ltd. (1963).Search in Google Scholar

[4] A. G. Radwan, A. M. Soliman, A. S. Elwakil, Design equations for fractional order sinusoidal oscillators: Four practical design examples. Intern. J. of Circuit Theory and Appl. 36, No 4 (2008), 473–492.10.1002/cta.453Search in Google Scholar

[5] A. Yüce, N. Tan, Electronic realisation technique for fractional order integrators, The J. of Engineering 2020, No 5 (2020), 157–167.10.1049/joe.2019.1024Search in Google Scholar

[6] A. Kartci, N. Herencsar, J. Tenreiro Machado, L. Brancik, History and progress of fractional order element passive emulators: A review. Radioengineering 29, No 2 (2020), 296–304.10.13164/re.2020.0296Search in Google Scholar

[7] A. Oustaloup, Fractional order sinusoidal oscillators: optimization and their use in highly linear modulation. IEEE Trans. on Circuit and Systems 28, No 10 (1981), 10–19.10.1109/TCS.1981.1084917Search in Google Scholar

[8] A. Oustaloup, F. Levron, B. Mathiew, F. Nanot, Frequency band complex noninteger differentiator: Characterization and synthesis. IEEE Trans. on Circuits and Systems I: Fundamental Theory and Appl. 47, No 1 (2000), 25–39.10.1109/81.817385Search in Google Scholar

[9] A. M. Elshurafa, M. N. Almadhoun, K. N. Salama, H. N. Alshareef, Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites. Appl. Phys. Letters 102 (2013), 232901–232904.10.1063/1.4809817Search in Google Scholar

[10] A. Djouambi, A. Charef, A. V. Besancon, Optimal approximation simulation and analog realization of the fundamental fractional order transfer function. Intern. J. of Appl. Math. and Computer Sci. 17, No 4 (2007), 455–462.10.2478/v10006-007-0037-9Search in Google Scholar

[11] A. Agambayev, Design fabrication and application of fractional order capacitors. PhD Thesis, King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia (2019).Search in Google Scholar

[12] B. Kishore, I. Noh Karsiti, Hassam, and Harindran, Frequency response based curve fitting approximation of fractional order PID controllers. Intern. J. of Appl. Math. and Computer Sci. 29, No 2 (2019), 311–326.Search in Google Scholar

[13] B. Mathieu, P. Melchior, A. Oustaloup, C. Ceyral, Fractional differentiation for edge detection. Fract. Signal Processing and Appl. 83, No 11 (2003), 2285–2480.10.1016/S0165-1684(03)00194-4Search in Google Scholar

[14] B. Maundy, A. S. Elwakil, S. Gift, On a multivibrator that employs a fractional capacitor. Analog Integrated Circuits and Signal Processing 62, No 1 (2010), 99–103.10.1007/s10470-009-9329-3Search in Google Scholar

[15] B.T. Krishna, K.V.V.S. Reddy, Analysis of fractional order lowpass and highpass filters. J. of Electr. Engineering 8, No 1 (2008), 1–5.Search in Google Scholar

[16] B.T. Krishna, K.V.V.S. Reddy, S. Santha Kumari, Time domain response calculations of fractance device of order 1/2. J. of Active and Passive Electr. Devices 3, No 3 (2008), 355–367.Search in Google Scholar

[17] B.T. Krishna, K.V.V.S. Reddy, Active and passive realization of fractance device of order 1/2. J. of Active and Passive Electr. Components 2008 (2008), 1–5; 10.1155/2008/369421.Search in Google Scholar

[18] B.T. Krishna, Studies on fractional order differentiators and integrators: A survey. Signal Processing 91, No 3 (2011), 386–426.10.1016/j.sigpro.2010.06.022Search in Google Scholar

[19] B.T. Krishna, K.V.V.S. Reddy, Design of fractional order digital differentiators and integrators using indirect discretization. Fract. Calc. Appl. Anal. 11, No 2 (2008), 1143–1151.Search in Google Scholar

[20] D. Mondal and K. Biswas, Packaging of single component fractional order element. IEEE Trans. on Device and Materials Reliability 13, No 1 (2013), 73–80.10.1109/TDMR.2012.2212020Search in Google Scholar

[21] R. El-Khazali, I. M. Batiha, and S. Momani, Approximation of fractional order operators. In: Intern. Workshop on Advanced Theory and Appl. of Fractional Calculus, Jordan (2018), 121–151.10.1007/978-981-15-0430-3_8Search in Google Scholar

[22] E. M. Hamed, Amr M. AbdelAty, L. A. Said, A. G. Radwan, Effect of different approximation techniques on fractional-order KHN filter design. Circuits Systems and Signal Processing 37 (2018), 5222–5252.10.1007/s00034-018-0833-5Search in Google Scholar

[23] E. Piotrowska, K. Rogowski, Time domain analysis of Fractional electrical circuit containing two ladder elements. Electronics 10, No 475 (2021), 1–13.10.3390/electronics10040475Search in Google Scholar

[24] G. Bohannan, Application of fractional calculus to polarization dynamics in solid dielectric materials. PhD Thesis, Montana State Univ., Bozeman, USA (2000).Search in Google Scholar

[25] G. E. Carlson, C. A. Halijak, Approximation of a fractional capacitors (1s)1n by a regular Newton process. IEEE Trans. on Circuit and Systems 11, No 2 (1964), 210–213.Search in Google Scholar

[26] G. Tsirimokou, C. Psychalinos, Ultra low voltage fractional-order differentiator and integrator topologies: an application for handling noisy ECGs. Analog Integrated Circuits and Signal Processing 81, No 2 (2014), 393–405.10.1007/s10470-014-0391-0Search in Google Scholar

[27] G. Tsirimokou, C. Psychalinos, A. S. Elwakil, Emulation of a constant phase element using operational transconductance amplifiers. Analog Integrated Circuits and Signal Processing 85, No 3 (2015), 413–423; 10.1007/s10470-015-0626-8.Search in Google Scholar

[28] G. Tsirimokou, A. Kartci, J. Koton, N. Herencsar, C. Psychalinos, Comparative study of discrete component realizations of fractional order capacitor and inductor active emulators. J. of Circuits Systems and Computers 27, No 11 (2018), 1850170-1–1850170-26.10.1142/S0218126618501700Search in Google Scholar

[29] G. W. Bohannan, Analog realization of a fractional control element revisited. In: Proc. of the 41st IEEE Intern. Conf. on Decision and Control, Las Vegas (2002), 1–4.Search in Google Scholar

[30] G. Liang, J. Hao, D. Shan, Electromagnetic interpretation of fractional order elements. J. of Modern Physics 8, No 14 (2017), 2209–2218.10.4236/jmp.2017.814136Search in Google Scholar

[31] I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).Search in Google Scholar

[32] I. Petras, The fractional order controllers: methods for their synthesis and application. J. of Electr. Engineering 50, No 9–10 (1999), 284–288.Search in Google Scholar

[33] I. Podlubny, Fractional order systems and PI^λD^μcontrollers. IEEE Trans. on Automatic Control 44, No 1 (1999), 208–214.10.1109/9.739144Search in Google Scholar

[34] I. S. Jesus, R. S. Barbosa, J. A. T. Machado, J. B. Cunha, Strategies for the control of heat diffusion systems based on fractional calculus. In: IEEE Intern. Conf. on Computational Cybernetics (ICCC’06), Budapest, Hungary (2006), 1–6.10.1109/ICCCYB.2006.305716Search in Google Scholar

[35] I. S. Jesus and J. A. T. Machado, Development of fractional order capacitors based on electrolyte processes. Nonlinear Dynamics 56, No 1 (2009), 45–55.10.1007/s11071-008-9377-8Search in Google Scholar

[36] K. B. Oldham and J. Spanier, The Fractional Calculus. Academic Press, New York (1974).Search in Google Scholar

[37] K. Biswas, S. Sen, P. K. Dutta, Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans. on Circuit and Systems–II: Express Briefs 53, No 9 (2006), 802–806.10.1109/TCSII.2006.879102Search in Google Scholar

[38] K. Matsuda, H. Fujii, H1 optimized wave absorbing control: analytical and experimental results. J. of Guidance Control and Dynamics 16, No 6 (1993), 1146–1153.10.2514/3.21139Search in Google Scholar

[39] L. Debnath, Recent applications of fractional calculus to science and engineering. Intern. J. of Math. and Math. Sci. 54 (2003), 3413–3446.10.1155/S0161171203301486Search in Google Scholar

[40] M. Nakagawa, K. Sorimachi, Basic characteristics of a fractance device. IEICE Trans. on Fundamental Electr. Communication and Computer Sci. E75-A, No 12 (1992), 1814–1819.Search in Google Scholar

[41] M. Sugi, Y. Hirano, Y. F. Miura and K. Saito, Simulation of fractal immittance by analog circuits: An approach to the optimized circuits. IEICE Trans. Fundam. Electron.Commun. Comput. Sci E82-A, No 8 (1999), 1627–1635.Search in Google Scholar

[42] M. F. Silva, J. A. T. Machado, A. M. Lopes, Comparison of fractional and integer order control of an hexapod robot. In: 19th Biennial Conf. on Mech. Vibration and Noise, Chicago (2003), 667–676.10.1115/DETC2003/VIB-48377Search in Google Scholar

[43] M. F. Silva, J. A. T. Machado, A. M. Lopes, Position/force control of a walking robot. Machine Intelligence and Robot Control 5, No 2 (2003), 33–44.Search in Google Scholar

[44] M. R. Dar, N. A. Kant, F. A. Khanday, C. Psychalinos, Fractional-order filter design for ultra low frequency applications. In: IEEE Intern. Conf. on Recent Trends in Electronics, Information and Communication Technology (IEEE-RTEICT-2016), Bengaluru (2016), 1727–1730.10.1109/RTEICT.2016.7808129Search in Google Scholar

[45] Pu Yifei, Yuan Xiao, Liao Ke, Zhou Jiliu, Zhang Ni, Pu Xiaoxian, Zeng Yi, A recursive two circuits series analog fractance circuit for any order fractional calculus. In: Proc. of the SPIE, China (2006), 509–519.10.1117/12.668189Search in Google Scholar

[46] R. Caponetto, S. Graziani, F. L. Pappalardo, and F. Sapuppo, Experimental characterization of ionic polymer metal composite as a novel fractional order element. Advanced Math. Physics 2013 (2013), 1–10.10.1155/2013/953695Search in Google Scholar

[47] S. Manabe, The non integer integral and its application to control systems. The J. of the Institute of Electr. Engineers of Japan 80, No 860 (1960), 589–597.Search in Google Scholar

[48] S. Westerlund, L. Ekstam, Capacitor theory. IEEE Trans. on Dielectr. Electr. Insul. 1, No 5 (1994), 826–839.10.1109/94.326654Search in Google Scholar

[49] S. C. Dutta Roy, On the realization of constant argument immitance or fractional operator. IEEE Trans. on Circuit and Systems 14, No 3 (1967), 264–274.Search in Google Scholar

[50] T. C. Haba, G. Ablart and T. Camps, The frequency response of a fractal photolithographic structure. IEEE Trans. on Dielectrics and Electr. Insulation 4, No 3 (1997), 321–326.10.1109/94.598289Search in Google Scholar

[51] T. J. Freeborn, B. Maundy, A. S. Elwakil, Field programmable analogue array implementation of fractional step filters. IET Circuits Devices and Systems 4, No 6 (2010), 514–524.10.1049/iet-cds.2010.0141Search in Google Scholar

[52] T. J. Freeborn, A survey of fractional order circuit models for biology and biomedicine. IEEE J. on Emerging and Selected Topics in Circuits and Systems 3, No 3 (2013), 416–423.10.1109/JETCAS.2013.2265797Search in Google Scholar

[53] W. Ahmad, R. El-Khazali, Fractional-order passive low pass flters. In: Proc. of the 2003 10th IEEE Intern. Conf. on Electronics Circuits and Systems, United Arab Emirates (2003), 160–163.Search in Google Scholar

[54] W. Ahmad, R. El Khazali, A. S. Elwakil, Fractional order Weinbridge oscillator. Electronics Letters 37, No 18 (2001), 1110–1112.10.1049/el:20010756Search in Google Scholar

[55] Z. M. Shah, M. Y. Kathjoo, F. A. Khanday, K. Biswas, C. Psychalinos, A survey of single and multi-component Fractional Order Elements (FOEs) and their applications. Microelectronics J. 48, (2019), 9–25.10.1016/j.mejo.2018.12.010Search in Google Scholar