Jos´e Francisco AGUILAR GOMEZ

Behavior characteristics of a cap-resistor, memcapacitor, and a memristor from the response obtained of RC and RL electrical circuits described by fractional differential equations

This paper provides an analysis of RC and RL electrical circuits described by a fractional difierential equation of Caputo type. The order considered is 0

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[1] Nasrolahpour H. Time fractional formalism: classical and quantum phenomena. PST J 2012; 3: 99-108.
[2] Oldham KB, Spanier J. The Fractional Calculus. New York, NY, USA: Academic Press, 1974.
[3] Miller KS, Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. New York, NY, USA: Wiley, 1993.
[4] Podlubny I. Fractional Differential Equations. New York, NY, USA: Academic Press, 1999.
[5] Hilfer R. Applications of Fractional Calculus in Physics. Singapore: World Scientific, 2000.
[6] G´omez JF. Comparison of the fractional response of a RLC network and RC circuit. PST J 2012; 3: 736-742.
[7] Magin RL. Fractional Calculus in Bioengineering. Danbury, CT, USA: Begell House, 2006.
[8] Baleanu D, G¨unvenc ZB, Tenreiro Machado JA. New Trends in Nanotechnology and Fractional Calculus Applications. Dordrecht, the Netherlands: Springer, 2010.
[9] Obeidat A, Gharibeh M, Al-Ali M, Rousan A. Evolution of a current in a resistor. Fract Calc App Anal 2011; 14: 247-259.
[10] Petras I. Fractional-order memristor-based Chuas circuit. IEEE T Circuits-II 2010; 57: 975-979.
[11] Johnsen GK. An introduction to the memristor a valuable circuit element in bioelectricity and bioimpedance. J Electr Bioimp 2012; 3: 20-28.
[12] Jimenez-Fernandez VM, Dominguez-Chavez JA, Vazquez-Leal H, Gallardo del Angel A, Hernandez-Paxtian ZJ. Descripci´on del modelo el´ectrico del memristor. Rev Mex F´ıs E 2012; 58: 113-119 (in Spanish).
[13] Pabst O, Schmidt T. Frequency dependent rectifier memristor bridge used as a programmable synaptic membrane voltage generator. J Electr Bioimp 2013; 4: 23-32.
[14] Reyes-Melo ME, Martinez-Vega JJ, Guerrero-Salaz´ar CA, Ortiz-Mendez U. Application of fractional calculus to modeling of relaxation phenomena of organic dielectric materials. In: IEEE 2004 International Conference on Solid Dielectrics; 59 July 2004; Toulouse, France. New York, NY, USA: IEEE. pp. 530-533.
[15] G´omez F, Bernal J, Rosales J, C´ordova T. Modeling and simulation of equivalent circuits in description of biological systemsa fractional calculus approach. J Electr Bioimp 2012; 3: 2-11.
[16] Reyes-Melo ME, Martinez-Vega JJ, Guerrero-Salaz´ar CA, Ortiz-Mendez U. Modelling of relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order. J Optoelectron Adv M 2004; 6: 1037-1043.
[17] Driscoll T, Kim HT, Chae BG, Kim BJ, Lee YW, Jokerst NM, Palit S, Smith DR, Di Ventra M, Basov DN. Memory metamaterials. Science 2009; 325: 1518-1521.
[18] Di Ventra M. Electrical Transport in Nanoscale Systems. Cambridge, UK: Cambridge University Press, 2008.
[19] Di Ventra M, Pershin Y, Chua L. Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc IEEE 2009; 97: 1717-1724.
[20] Fouda ME, Radwan AG, Salama KN. Effect of boundary on controlled memristor-based oscillator. In: IEEE 2012 International Conference on Engineering and Technology; 1011 October 2012; Cairo, Egypt. New York, NY, USA: IEEE. pp. 1-5.
[21] Jo S, Chang T, Ebong I, Bhadviya B, Mazumder P, Lu W. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett 2010; 10: 1297-1301.
[22] Di Ventra M, Pershin YV, Chua L. Circuit elements with memory: memristors, memcapacitors and meminductors. Proc IEEE 2009; 97: 1717-1724.
[23] Pershin YV, Di Ventra M. Memristive circuits simulate memcapacitors and meminductors. Proc IEEE 2009; 97: 517-528.
[24] Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calc Appl Anal 2002; 5: 367-386.
[25] Moshre-Torbati M, Hammond JK. Physical and geometrical interpretation of fractional operators. J Franklin I 1998; 335: 1077-1086.