[1] J.F. Gomez-Aguilar, J.J. Rosales-Garcia, J.J. Bernal-Alvarado, et al., “Fractional mechanical oscillators”, Revista Mexicana de Fisica, vol. 58, pp. 348–352, 2012.
[2] K. Diethelm, D. Baleanu, E. Scalas, J.J. Trujillo, “Fractional Calculus: Models and Numerical Methods”, 2 Ed., Singapore: World Scientific, 2016.
[3] I. Podlubny, “Fractional Differential Equations”, vol. 198, Academic Press, Boston, 1999.
[4] S. Zheng, W. Li, “Robust stabilization of fractional-order plant with general interval uncertainties based on graphical method”, International Journal of Robust and Nonlinear Control, vol. 28, pp. 1672-1692, 2018.
[5] A Pratap, R Raja, C Sowmiya, et all. “Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses”, Neural Networks, vol. 103, pp. 128-141, 2018.
[6] V.A. Vyawahare, G. Espinosa-Paredes, “On the stability of linear fractional-space neutron point kinetics (F-SNPK) models for nuclear reactor dynamics”,Annals of Nuclear Energy,vol. 111, pp. 12–21, 2018.
[7] A. Karthikeyan, K. Rajagopal ,“FPGA implementation of fractional-order discretememristor chaotic system and its commensurate and incommensurate synchronizations”, J. Phys., vol. 90, pp. 1-13, 2018.
[8] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, “Theory and Applications of Fractional Differential Equations”, North-Holland Mathematical Studies, Vol. 204, Elsevier, Amsterdam, 2006.
[9] J. Ma, P. Zhou, B. Ahmad, et. all, “Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor”, PloS One, vol. 13, pp. 1-21, 2018.
[10] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, “Transient chaos in fractional Bloch equations, Computers and Mathematics with Applications”, vol. 64, pp. 3367-3376, 2012.
[11] J. Dvorak, L. Langhammer, at. all, “Synthesis and analysis of electronically adjustable fractional-order low-pass filter”, Journal of Circuits, Systems and Computers,vol. 27, DOI: S0218126618500329,2018.
[12] J. Dvorak, Z. Polesakova, at. all, “Non-Integer-Order Low-Pass Filter with Electronically Controllable Parameters”, IEEE-Xplore, DOI: 978-1-5386-4881-0/18, 2018.
[13] G. Liang, Y. Jing, at. all, “Passive synthesis of a class of fractional immittance function based on multivariable theory”, Journal of Circuits, Systems and Computers, vol. 27, DOI: 10.1142/S0218126618500743, 2018.
[14] A. Agambayev, K.H. Rajab, Towards fractional-order capacitors with broad tunable constant phase angles: multi-walled carbon nanotube-polymer composite as a case study, Journal of Physics D: Applied Physics,vol.51, pp. 1-6, 2018
[15] A. Jakubowska-Ciszek, J. Walczak, “Analysis of the transient state in a parallel circuit of the class RLβCα”, Applied Mathematics and Computation, vol. 319, pp. 287-300, 2018.
[16] P. Bertsias, C. Psychallions, at. all, “Differentiator based fractional-order high-pass filter designs”, Proceedings of the 7th International Conference on Modern Circuits and Systems Technologies (MOCAST), Article ID: 17840792, 2018.
[17] F. Gomez, J. Rosales, M. Guia, “RLC electrical circuits of non-integer order”, Central European Journal of Physics, vol. 11, pp. 1361-1365, 2013.
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Fractional Order Butterworth Filter

( Vol-5,Issue-12,December 2018 ) OPEN ACCESS
Author(s):

Mehmet Emir Koksal

Keywords:

Butterworth filter, control system, fractional order.

Abstract:

[1] J.F. Gomez-Aguilar, J.J. Rosales-Garcia, J.J. Bernal-Alvarado, et al., “Fractional mechanical oscillators”, Revista Mexicana de Fisica, vol. 58, pp. 348–352, 2012.
[2] K. Diethelm, D. Baleanu, E. Scalas, J.J. Trujillo, “Fractional Calculus: Models and Numerical Methods”, 2 Ed., Singapore: World Scientific, 2016.
[3] I. Podlubny, “Fractional Differential Equations”, vol. 198, Academic Press, Boston, 1999.
[4] S. Zheng, W. Li, “Robust stabilization of fractional-order plant with general interval uncertainties based on graphical method”, International Journal of Robust and Nonlinear Control, vol. 28, pp. 1672-1692, 2018.
[5] A Pratap, R Raja, C Sowmiya, et all. “Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses”, Neural Networks, vol. 103, pp. 128-141, 2018.
[6] V.A. Vyawahare, G. Espinosa-Paredes, “On the stability of linear fractional-space neutron point kinetics (F-SNPK) models for nuclear reactor dynamics”,Annals of Nuclear Energy,vol. 111, pp. 12–21, 2018.
[7] A. Karthikeyan, K. Rajagopal ,“FPGA implementation of fractional-order discretememristor chaotic system and its commensurate and incommensurate synchronizations”, J. Phys., vol. 90, pp. 1-13, 2018.
[8] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, “Theory and Applications of Fractional Differential Equations”, North-Holland Mathematical Studies, Vol. 204, Elsevier, Amsterdam, 2006.
[9] J. Ma, P. Zhou, B. Ahmad, et. all, “Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor”, PloS One, vol. 13, pp. 1-21, 2018.
[10] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, “Transient chaos in fractional Bloch equations, Computers and Mathematics with Applications”, vol. 64, pp. 3367-3376, 2012.
[11] J. Dvorak, L. Langhammer, at. all, “Synthesis and analysis of electronically adjustable fractional-order low-pass filter”, Journal of Circuits, Systems and Computers,vol. 27, DOI: S0218126618500329,2018.
[12] J. Dvorak, Z. Polesakova, at. all, “Non-Integer-Order Low-Pass Filter with Electronically Controllable Parameters”, IEEE-Xplore, DOI: 978-1-5386-4881-0/18, 2018.
[13] G. Liang, Y. Jing, at. all, “Passive synthesis of a class of fractional immittance function based on multivariable theory”, Journal of Circuits, Systems and Computers, vol. 27, DOI: 10.1142/S0218126618500743, 2018.
[14] A. Agambayev, K.H. Rajab, Towards fractional-order capacitors with broad tunable constant phase angles: multi-walled carbon nanotube-polymer composite as a case study, Journal of Physics D: Applied Physics,vol.51, pp. 1-6, 2018
[15] A. Jakubowska-Ciszek, J. Walczak, “Analysis of the transient state in a parallel circuit of the class RLβCα”, Applied Mathematics and Computation, vol. 319, pp. 287-300, 2018.
[16] P. Bertsias, C. Psychallions, at. all, “Differentiator based fractional-order high-pass filter designs”, Proceedings of the 7th International Conference on Modern Circuits and Systems Technologies (MOCAST), Article ID: 17840792, 2018.
[17] F. Gomez, J. Rosales, M. Guia, “RLC electrical circuits of non-integer order”, Central European Journal of Physics, vol. 11, pp. 1361-1365, 2013.

ijaers doi crossref DOI:

10.22161/ijaers.5.12.25

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