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The RC Circuit Described by Local Fractional Differential Equations

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Języki publikacji
EN
Abstrakty
EN
A non-differentiable resistor-capacitor circuit comprised of the capacitor and resistor in the fractal-time domain is first proposed in this article. The solution behavior of the corresponding local fractional ordinary differential equation is presented for the Mittag-Leffler decay defined on Cantor sets. The obtained results reveal the sufficiency of the local fractional calculus in the analysis of the fractal electrical systems.
Wydawca
Rocznik
Strony
419--429
Opis fizyczny
Bibliogr. 35 poz., rys., tab., wykr.
Twórcy
autor
  • IoT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China
autor
  • School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, People’s Republic of China
autor
  • IoT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China
autor
  • Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China
Bibliografia
  • [1] Caponetto R. Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore, 2010. ISBN: 9814304204, 9789814304207.
  • [2] Odibat Z, Corson N, Aziz-Alaoui M, Bertelle C. Synchronization of chaotic fractional-order systems via linear control, International Journal of Bifurcation and Chaos, 2010; 20: 81-97. doi: 10.1142/S0218127410025429.
  • [3] Balachandran K, Park JY, Trujillo JJ. Controllability of nonlinear fractional dynamical systems, Nonlinear Analysis: Theory, Methods & Applications, 2012; 75 (4): 1919-1926. URL http://dx.doi.org/10.1016/j.na.2011.09.042.
  • [4] Frederico GS, Torres DF. Fractional conservation laws in optimal control theory, Nonlinear Dynamics, 2008; 53: 215-222. doi: 10.1007/s11071-007-9309-z.
  • [5] Machado JAT. Entropy analysis of integer and fractional dynamical systems, Nonlinear Dynamics, 2010; 62 (1): 371-378. doi; 10.1007/s11071-010-9724-4.
  • [6] Saichev AI, Zaslavsky GM. Fractional kinetic equations: solutions and applications, Chaos, 1997; 7 (4): 753-764. doi: 10.1063/1.166272.
  • [7] Gafiychuk V, Datsko B, Meleshko V. Mathematical modeling of time fractional reaction-diffusion systems, Journal of Computational and Applied Mathematics, 2008; 220 (l-2): 215-225. URL http://dx.doi.org/10.1016/j.cam.2007.08.011.
  • [8] Hilfer R. Fractional dynamics, irreversibility and ergodicity breaking, Chaos, Solitons and Fractals, 1995; 5 (8): 1475-1484. doi: 10.1016/0960-0779(95)00027-2.
  • [9] Hilfer R. Foundations of fractional dynamics, Fractals, 1995; 3 (3): 549-556. doi: 10.1142/S0218348X95000485.
  • [10] Achar BNN, Hanneken JW, Enck T, Clarke T. Dynamics of the fractional oscillator, Physica A, 2001; 297 (3-4): 361-367. URL http://dx.doi.org/10.1016/S0378-4371(01)00200-X.
  • [11] Lu JG. Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal, Chaos, Solitons and Fractals, 2006; 27 (2): 519-525. doi: 10.1016/j.chaos.2005.04.032.
  • [12] Ngueuteu GM, Woafo P. Dynamics and synchronization analysis of coupled fractional-order nonlinear electromechanical systems, Mechanics Research Communications, 2012; 46: 20-25. URL http://dx.doi.org/10.1016/j.mechrescom.2012.08.003.
  • [13] Baleanu D, Machado JAT, Luo AC. Fractional Dynamics and Control, Springer, New York, 2011. ISBN: 1461404568 9781461404569.
  • [14] Machado JAT. Fractional generalization of memristor and higher order elements, Communications in Nonlinear Science and Numerical Simulation, 2013; 18 (2): 264-275. URL http://dx.doi.org/10.1016/j.cnsns.2012.07.014.
  • [15] Martynyuk V, Ortigueira M. Fractional model of an electrochemical capacitor, Signal Processing, 2015; 107: 355-360. URL http://dx.doi.org/10.1016/j.sigpro.2014.02.021.
  • [16] Hartley TT, Veillette RJ, Adams JL, et al. Energy storage and loss in fractional-order circuit elements, IET Circuits, Devices and Systems, 2015; 9 (3): 227-235. doi: 10.1049/iet-cds.2014.0132.
  • [17] Jesus IS, Machado JAT. Comparing integer and fractional models in some electrical systems. In: Proceedings of the 4th IFAC Workshop on Fractional Differentiation and Its Applications (FDA’ 10), Badajoz, Spain, October 18-20, pp. 1-6, 2010. ISBN: 9788055304878.
  • [18] Radwan AG, Soliman AM, Elwakil AS. First-order filters generalized to the fractional domain, Journal of Circuits, Systems, and Computers, 2008; 17 (l): 55-66. doi: 10.1142/S0218126608004162.
  • [19] Chen P, He S. Analysis of the fractional-order parallel tank circuit, Journal of Circuits, Systems, and Computers, 2013; 22 (3): 1350047. doi: 10.1142/S0218126613500473.
  • [20] Radwan AG, Salama KN. Fractional-order RC and RL circuits, Circuits, Systems, and Signal Processing, 2012; 31 (6): 1901-1915. doi: 10.1007/s00034-012-9432-z.
  • [21] Guia M, Gómez F, Rosales J. Analysis on the time and frequency domain for the RC electric circuit of fractional order, Open Physics, 2013; 11 (10): 1366-1371. doi: 10.2478/s11534-013-0236-y.
  • [22] Mitkowski W, Skruch P. Fractional-order models of the supercapacitors in the form of RC ladder networks, Bulletin of the Polish Academy of Sciences: Technical Sciences, 2013; 61 (3): 581-587. URL https://doi.org/10.2478/bpasts-2013-0059.
  • [23] Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Vol. 204, Amsterdam, London and New York: Elsevier (North- Holland) Science Publishers, 2006. ISBN: 0444518320.
  • [24] Cattani C, Srivastava HM, Yang XJ. Fractional Dynamics, Emerging Science Publishers, Berlin, 2016. ISBN: 978-3-11-047209-7.
  • [25] Yang XJ, Baleanu D, Srivastava HM. Local Fractional Integral Transforms And Their Applications, (1rd edition), Academic Press, New York, 2015. ISBN: 978-0-12-804002-7.
  • [26] Yang XJ, Baleanu D, Srivastava HM. Local fractional similarity solution for the diffusion equation defined on Cantor sets, Applied Mathematics Letters, 2015; 47: 54-60. URL http://dx.doi.org/10.1016/j.aml.2015.02.024.
  • [27] Yang XJ, Machado JAT, Hristov J. Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow, Nonlinear Dynamics, 2015, doi: 10.1007/s11071-015-2085-2.
  • [28] Yang XJ, Srivastava HM. An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Communications in Nonlinear Science and Numerical Simulation, 2015; 29 (l-3): 499-504. URL http://dx.doi.org/10.1016/j.cnsns.2015.06.006.
  • [29] Yang XJ, Srivastava HM, He JH, Baleanu D. Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives, Physics Letters A, 2013; 377 (28-30): 1696-1700. URL http://dx.doi.org/10.1016/j.physleta.2013.04.012.
  • [30] Yang XJ, Machado JAT, Cattani C. A new model of the LC-electric circuit modelled by local fractional calculus, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, 2015, In press.
  • [31] Yang XJ, Baleanu D, Machado JAT. Application of the local fractional Fourier series to fractal signals, in: Machado, J. T., Baleanu, D., and Luo, A. -C. (eds), Discontinuity and Complexity in Nonlinear Physical Systems, New York, Springer, pp. 63-89, 2014. doi: 10.1007/978-3-319-01411-1_4.
  • [32] Zhang YD, Chen SF. Magnetic resonance brain image classification based on weighted-type fractional Fourier transform and nonparallel support vector machine, International Journal of Imaging Systems and Technology, 2015; 24 (4): 317-327. doi: 10.1002/ima.22144.
  • [33] Wang SH, Zhang YD, Sun P. Pathological Brain Detection by a Novel Image Feature - Fractional Fourier Entropy, Entropy, 2015; 17 (12): 8278-8296. doi: 10.3390/e17127877.
  • [34] Liu G, Yang JQ. Computer-aided Diagnosis of Abnormal Breasts in Mammogram Images by Weighted-Type Fractional Fourier Transform, Advances in Mechanical Engineering, 2016; 8 (2): 1-11. doi: 10.1177/1687814016634243.
  • [35] Carlo C, Rao RV. Tea Category Identification Using a Novel Fractional Fourier Entropy and Jaya Algorithm Entropy, 2016; 18 (3): 77. doi: 10.3390/e18030077.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4efc2555-aa22-4df8-9690-f7f5f422185f
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