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Abstrakty
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
Czasopismo
Rocznik
Tom
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