A class of fractal-chain fractance approximation circuit

References

• AbdelAty, A. M., Elwakil, A. S., Radwan, A. G., Psychalinos, C., & Maundy, B. (2018). Approximation of the fractional-order laplacian sα as a weighted sum of first-order high-pass filters. IEEE Transactions on Circuits and Systems II: Express Briefs, 65(8), 1114–1118.
   Web of Science ®Google Scholar
• Atan, O. (2018). Implementation and simulation of fractional order chaotic circuits with time-delay. Analog Integrated Circuits and Signal Processing, 96(3), 485–494.
   Web of Science ®Google Scholar
• Bertsias, P., Psychalinos, C., Elwakil, A., & Maundy, B. (2017). Current-mode capacitor- less integrators and differentiators for implementing emulators of fractional-order elements. AEU-International Journal of Electronics and Communications, 80, 94–103.
   Web of Science ®Google Scholar
• Bertsias, P., Psychalinos, C., Radwan, A. G., & Elwakil, A. S. (2018). High-frequency capacitorless fractional-order cpe and fi emulator. Circuits, Systems, and Signal Processing, 37(7), 2694–2713.
   Web of Science ®Google Scholar
• Carlson, G., & Halijak, C. (1962, Sep.). Approximations of fixed impedances. IRE Trans. Circuit Theory, 9(3), 302–303.
   Google Scholar
• Carlson, G., & Halijak, C. (1964). Approximation of fractional capacitors (1/s)1/n by a regular newton process. IEEE Transactions on Circuit Theory, 11(2), 210–213.
   Google Scholar
• Carlson, G. E. (1960). Simulation of the fractional derivative operator √s and the fractional integral operator 1/√s. (Master’s thesis). Kansas State University.
   Google Scholar
• Charef, A. (2006). Analogue realisation of fractional-order integrator, differentiator and fractional P IλDµ controller. IEE Proceedings-Control Theory and Applications, 153(6), 714–720.
   Google Scholar
• Chen, D., Liu, C., Wu, C., Liu, Y., Ma, X., & You, Y. (2012). A new fractional-order chaotic system and its synchronization with circuit simulation. Circuits Systems and Signal Processing, 31(5), 1599–1613.
   Web of Science ®Google Scholar
• Dar, M. R., Kant, N. A., & Khanday, F. A. (2017). Electronic implementation of fractional- order Newton-Leipnik chaotic system with application to communication. Journal of Com- Putational and Nonlinear Dynamics, 12, 054502.
   Web of Science ®Google Scholar
• El-Sayed, A. M. A., Nour, H. M., Elsaid, A., Matouk, A. E., & Elsonbaty, A. (2015). Dynamical behaviors, circuit realization, chaos control and synchronization of a new fractional order hyperchaotic system. Applied Mathematical Modelling, 40(5), 3516–3534.
   Web of Science ®Google Scholar
• He, Q. Y., Pu, Y. F., Yu, B., & Yuan, X. (2019). Scaling fractal-chuan fractance approximation circuits of arbitrary order. Circuits, Systems, and Signal Processing, 38(11), 4933–4958.
   Web of Science ®Google Scholar
• He, Q. Y., Pu, Y. F., Yu, B., & Yuan, X. (submitted for publication). Scaling fractal-ladder fractance approximation circuits of arbitrary order.
   Google Scholar
• He, Q. Y., Yu, B., & Yuan, X. (2017). Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order. Chinese Physics B, 26(4), 66–74.
   Web of Science ®Google Scholar
• He, Q. Y., & Yuan, X. (2016). Carlson iteration and rational approximations of arbitrary order fractional calculus operator. Acta Physica Sinica, 65(16), 25–34.
   Web of Science ®Google Scholar
• Izaguirre-Espinosa, C., Muñoz-Vázquez, A.-J., Sánchez-Orta, A., Parra-Vega, V., & Fantoni, I. (2019). Fractional-order control for robust position/yaw tracking of quadrotors with experiments. IEEE Transactions on Control Systems Technology, 27(4), 1645–1650.
   Web of Science ®Google Scholar
• Jesus, M.-P., Ernesto, Z.-S., Christos, V., Sajad, J., Jacques, K., & Karthikeyan, R. (2018). A new fractional-order chaotic system with different families of hidden and self-excited attractors. Entropy, 20(8), 564.
   PubMed Web of Science ®Google Scholar
• Jiang, Y., & Zhang, B. (2018). High-power fractional-order capacitor with 1 < α < 2 based on power converter. IEEE Transactions on Industrial Electronics, 65(4), 3157–3164.
   Web of Science ®Google Scholar
• Kadlčík, L., & Horskỳ, P. (2018). A cmos follower-type voltage regulator with a distributed- element fractional-order control. IEEE Transactions on Circuits and Systems I: Regular Papers, 65(9), 2753–2763.
   Web of Science ®Google Scholar
• Kapoulea, S., Psychalinos, C., Elwakil, A. S., & Radwan, A. G. (2019). One-terminal electronically controlled fractional-order capacitor and inductor emulator. AEU-International Journal of Electronics and Communications, 103, 32–45.
   Web of Science ®Google Scholar
• Kaslik, E., & Sivasundaram, S. (2012). Nonlinear dynamics and chaos in fractional-order neural networks. Neural Networks, 32(1), 245–256.
   PubMed Web of Science ®Google Scholar
• Khattab, K. H., Madian, A. H., & Radwan, A. G. (2016, Oct.). CFOA-based fractional order simulated inductor. In 2016 IEEE 59th international midwest symposium on circuits and systems (MWSCAS) (pp. 16-19). Abu Dhabi, United Arab Emirates.
   Google Scholar
• Kubanek, D., Freeborn, T., & Koton, J. (2019). Fractional-order band-pass filter design using fractional-characteristic specimen functions. Microelectronics Journal, 86, 7786.
   Web of Science ®Google Scholar
• Liang, G. S., Jing, Y. M., Liu, C., & Ma, L. (2018). Passive synthesis of a class of fractional immittance function based on multivariable theory. Journal of Circuits, Systems and Computers, 27(05), 1850074.
   Web of Science ®Google Scholar
• Liu, P., Zeng, Z., & Wang, J. (2017). Multiple mittag-leffler stability of fractional-order recurrent neural networks. IEEE Transactions on Systems Man and Cybernetics Systems, 47(8), 2279–2288.
   Web of Science ®Google Scholar
• Liu, S. H. (1985). Fractal model for the ac response of a rough interface. Physical Review Letters, 55(5), 529–532.
   PubMed Web of Science ®Google Scholar
• Machado, J. A. T. (2001). Discrete-time fractional-order controllers. Journal of Fractional Calculus and Applied Analysis, 4(1), 47–66.
   Google Scholar
• Matsuda, K., & Fujii, H. (1993). H∞ optimized wave-absorbing control: Analytical and experimental results. Journal of Guidance Control and Dynamics, 16(6), 1146–1153.
   Web of Science ®Google Scholar
• Oldham, K. B. (1973). Semiintegral electroanalysis: Analog implementation. Analytical Chemistry, 45(1), 39–47.
   Web of Science ®Google Scholar
• Oustaloup, A., Cois, O., Lanusse, P., Melchior, P., Moreau, X., & Sabatier, J. (2006). The crone approach: Theoretical developments and major applications. IFAC Proceedings Volumes, 39(11), 324–354.
   Google Scholar
• Pu, Y. F. (2016a). Analog circuit realization of arbitrary-order fractional Hopfield neural networks: A novel application of fractor to defense against chip cloning attacks. IEEE Access, 4(99), 5417–5435.
   Web of Science ®Google Scholar
• Pu, Y. F. (2016b). Measurement units and physical dimensions of fractance-part II: Fractional- order measurement units and physical dimensions of fractance and rules for fractors in series and parallel. IEEE Access, 4, 3398–3416.
   Web of Science ®Google Scholar
• Pu, Y. F., Yi, Z., & Zhou, J. L. (2017). Fractional Hopfield neural networks: Fractional dynamic associative recurrent neural networks. IEEE Transactions on Neural Networks and Learning Systems, 28(10), 2319–2333.
   PubMed Web of Science ®Google Scholar
• Pu, Y. F., Yuan, X., Liao, K., & Zhou, J. L. (2006). Implement any fractional order neural-type pulse oscillator with net-grid type analog fractance circuit. Journal of Sichuan University (Engineering Science Edition), 38(1), 128–132.
   Google Scholar
• Pu, Y. F., Yuan, X., Liao, K., Zhou, J. L., Zhang, N., Zeng, Y., & Pu, X. X. (2005, Oct.). Structuring analog fractance circuit for 1/2 order fractional calculus. In 2005 6th international conference on ASIC (pp.  24-27). Shanghai, China.
   Google Scholar
• Pu, Y. F., Yuan, X., & Yu, B. (2018). Analog circuit implementation of fractional-order memristor: Arbitrary-order lattice scaling fracmemristor. IEEE Transactions on Circuits and Systems I: Regular Papers, 65(9), 2903–2916.
   Web of Science ®Google Scholar
• Qiang, H., Liu, C. X., Lei, S., & Zhu, D. R. (2013). A fractional order hyperchaotic system derived from a Liu system and its circuit realization. Chinese Physics B, 22(2), 133–138.
   Web of Science ®Google Scholar
• Sakthivel, R., Ahn, C. K., & Joby, M. (2019). Fault-tolerant resilient control for fuzzy fractional order systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(9), 1797-1805.
   Google Scholar
• Shahvali, M., Naghibi-Sistani, M.-B., & Modares, H. (2019). Distributed consensus control for a network of incommensurate fractional-order systems. IEEE Control Systems Letters, 3(2), 481–486.
   Google Scholar
• Tsirimokou, G., Psychalinos, C., Elwakil, A. S., & Salama, K. N. (2018). Electronically tunable fully integrated fractional-order resonator. IEEE Transactions on Circuits and Systems II: Express Briefs, 65(2), 166–170.
   Web of Science ®Google Scholar
• Wang, X., Kingni, S. T., Volos, C., Pham, V.-T., Vo Hoang, D., & Jafari, S. (2019). A fractional system with five terms: Analysis, circuit, chaos control and synchronization. International Journal of Electronics, 106(1), 109–120.
   Web of Science ®Google Scholar
• Wu, S. L., & Al-Khaleel, M. (2017). Parameter optimization in waveform relaxation for fractional-order RC circuits. IEEE Transactions on Circuits and Systems I: Regular Papers, 64(7), 1781–1790.
   Web of Science ®Google Scholar
• Xi, Y., Yu, Y., Zhang, S., & Hai, X. (2018). Finite-time robust control of uncertain fractional- order hopfield neural networks via sliding mode control. Chinese Physics B, 27(1), 010202.
   Web of Science ®Google Scholar
• Yang, S., Yu, J., Hu, C., & Jiang, H. (2018). Quasi-projective synchronization of fractional- order complex-valued recurrent neural networks. Neural Networks, 104, 104–113.
   PubMed Web of Science ®Google Scholar
• Yu, B., He, Q. Y., & Yuan, X. (2018). Scaling fractal-lattice franctance approximation circuits of arbitrary order and irregular lattice type scaling equation. Acta Physica Sinica, 67(7), 070202.
   Web of Science ®Google Scholar
• Yu, B, Pu, Y. F, He, Q. Y, & Yuan, X. (2020). Fractional-order dual-slope integral fast analog-to-digital converter with high sensitivity. journal of circuits. Systems and Computers, 29(5), 2050083. doi:10.1142/S0218126620500838
   Web of Science ®Google Scholar
• Yuan, X. (2015). Mathematical principles of fractance approximation circuits. Beijing: Science Press.
   Google Scholar
• Yuan, Z., & Yuan, X. (2017). On zero-pole distribution of regular RC fractal fractance approximation circuits. Acta Electronic Sinica, 45(10), 2511–2520.
   Google Scholar