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Volumn 25, Issue 1-3, 2015, Pages 10-18

Matrix fractional systems

Author keywords

Cole Cole; Davidson Cole; Fractional calculus; Fractional elements; Havriliak Negami

Indexed keywords

CALCULATIONS;

EID: 84924655799     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2015.01.006     Document Type: Article
Times cited : (20)

References (61)
  • 1
    • 80051619853 scopus 로고    scopus 로고
    • A poster about the recent history of fractional calculus
    • Machado J.A.T., Kiryakova V., Mainardi F. A poster about the recent history of fractional calculus. Fract Calc Appl Anal 2010, 13(3):329-334.
    • (2010) Fract Calc Appl Anal , vol.13 , Issue.3 , pp. 329-334
    • Machado, J.A.T.1    Kiryakova, V.2    Mainardi, F.3
  • 2
    • 80051619853 scopus 로고    scopus 로고
    • A poster about the old history of fractional calculus
    • Machado J.A.T., Kiryakova V., Mainardi F. A poster about the old history of fractional calculus. Frac Calc Appl Anal 2010, 13(4):447-454.
    • (2010) Frac Calc Appl Anal , vol.13 , Issue.4 , pp. 447-454
    • Machado, J.A.T.1    Kiryakova, V.2    Mainardi, F.3
  • 7
    • 77956684069 scopus 로고    scopus 로고
    • Theory and applications of fractional differential equations
    • Elsevier, Amsterdam
    • Kilbas A., Srivastava H., Trujillo J. Theory and applications of fractional differential equations. North-Holland Mathematics Studies 2006, vol. 204. Elsevier, Amsterdam.
    • (2006) North-Holland Mathematics Studies , vol.204
    • Kilbas, A.1    Srivastava, H.2    Trujillo, J.3
  • 11
    • 84855588363 scopus 로고    scopus 로고
    • Fractional Calculus for Scientists and Engineers
    • Springer, Dordrecht, Heidelberg
    • Ortigueira M.D. Fractional Calculus for Scientists and Engineers. Lecture Notes in Electrical Engineering 2011, Springer, Dordrecht, Heidelberg.
    • (2011) Lecture Notes in Electrical Engineering
    • Ortigueira, M.D.1
  • 17
    • 84879647927 scopus 로고    scopus 로고
    • Science metrics on fractional calculus development since 1966
    • Machado J.T., Galhano A.M., Trujillo J.J. Science metrics on fractional calculus development since 1966. Frac Calc Appl Anal 2013, 16(2):479-500.
    • (2013) Frac Calc Appl Anal , vol.16 , Issue.2 , pp. 479-500
    • Machado, J.T.1    Galhano, A.M.2    Trujillo, J.J.3
  • 18
    • 0004240239 scopus 로고
    • Chemical Catalog, New York
    • Debye P. Polar Molecules 1929, Chemical Catalog, New York.
    • (1929) Polar Molecules
    • Debye, P.1
  • 19
    • 84986400186 scopus 로고
    • Electric impedance of Asterias eggs
    • Cole K.S., Cole R.H. Electric impedance of Asterias eggs. J Gen Physiol 1936, 19(4):609-623.
    • (1936) J Gen Physiol , vol.19 , Issue.4 , pp. 609-623
    • Cole, K.S.1    Cole, R.H.2
  • 20
    • 84962011180 scopus 로고
    • Electric impedance of Arbacia eggs
    • Cole K.S., Cole R.H. Electric impedance of Arbacia eggs. J Gen Physiol 1936, 19(4):625-632.
    • (1936) J Gen Physiol , vol.19 , Issue.4 , pp. 625-632
    • Cole, K.S.1    Cole, R.H.2
  • 21
    • 33748565282 scopus 로고
    • Dispersion and absorption in dielectrics - I Alternating current characteristics
    • Cole K.S., Cole R.H. Dispersion and absorption in dielectrics - I Alternating current characteristics. J Chem Phys 1941, 9:341-352.
    • (1941) J Chem Phys , vol.9 , pp. 341-352
    • Cole, K.S.1    Cole, R.H.2
  • 22
    • 51149207143 scopus 로고
    • Dispersion and absorption in dielectrics - II Direct current characteristics
    • Cole K.S., Cole R.H. Dispersion and absorption in dielectrics - II Direct current characteristics. J Chem Phys 1942, 10:98-105.
    • (1942) J Chem Phys , vol.10 , pp. 98-105
    • Cole, K.S.1    Cole, R.H.2
  • 23
    • 0006042593 scopus 로고
    • Dielectric relaxation in glycerine
    • Davidson D.W., Cole R.H. Dielectric relaxation in glycerine. J Chem Phys 1950, 18:1417.
    • (1950) J Chem Phys , vol.18 , pp. 1417
    • Davidson, D.W.1    Cole, R.H.2
  • 24
    • 0345263918 scopus 로고
    • Dielectric relaxation in glycerol, propylene glycol, and npropanol
    • Davidson D.W., Cole R.H. Dielectric relaxation in glycerol, propylene glycol, and npropanol. J Chem Phys 1951, 19(12):1484-1490.
    • (1951) J Chem Phys , vol.19 , Issue.12 , pp. 1484-1490
    • Davidson, D.W.1    Cole, R.H.2
  • 25
    • 0001785405 scopus 로고
    • A complex plane analysis of α-dispersions in some polymer systems
    • Havriliak S., Negami S. A complex plane analysis of α-dispersions in some polymer systems. J Polym Sci Part C: Polym Sympos 1966, 14(1):99-117.
    • (1966) J Polym Sci Part C: Polym Sympos , vol.14 , Issue.1 , pp. 99-117
    • Havriliak, S.1    Negami, S.2
  • 26
    • 0344032495 scopus 로고
    • A complex plane representation of dielectric and mechanical relaxation processes in some polymers
    • Havriliak S., Negami S. A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 1967, 8(4):161-210.
    • (1967) Polymer , vol.8 , Issue.4 , pp. 161-210
    • Havriliak, S.1    Negami, S.2
  • 28
    • 0010174001 scopus 로고
    • On the realization of a constant-argument immitance of fractional operator
    • Roy S.C.D. On the realization of a constant-argument immitance of fractional operator. IEEE Trans Circuit Theory 1967, 14(3):264-374.
    • (1967) IEEE Trans Circuit Theory , vol.14 , Issue.3 , pp. 264-374
    • Roy, S.C.D.1
  • 30
    • 34047142616 scopus 로고    scopus 로고
    • Realization of a constant phase element and its performance study in a differentiator circuit
    • Biswas K., Sen S., Dutta P.K. Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans Circuits Syst II: Express Briefs 2006, 53(9):802-806.
    • (2006) IEEE Trans Circuits Syst II: Express Briefs , vol.53 , Issue.9 , pp. 802-806
    • Biswas, K.1    Sen, S.2    Dutta, P.K.3
  • 31
    • 52349114093 scopus 로고    scopus 로고
    • Analog fractional order controller in temperature and motor control applications
    • Bohannan G.W. Analog fractional order controller in temperature and motor control applications. J Vibr Control 2008, 14(9-10):1487-1498.
    • (2008) J Vibr Control , vol.14 , Issue.9-10 , pp. 1487-1498
    • Bohannan, G.W.1
  • 32
    • 61449144602 scopus 로고    scopus 로고
    • Development of fractional order capacitors based on electrolyte processes
    • Jesus I.S., Machado J.A.T. Development of fractional order capacitors based on electrolyte processes. Nonlinear Dyn 2009, 56(1-2):45-55.
    • (2009) Nonlinear Dyn , vol.56 , Issue.1-2 , pp. 45-55
    • Jesus, I.S.1    Machado, J.A.T.2
  • 33
    • 84858707796 scopus 로고    scopus 로고
    • Fractional order inductive phenomena based on the skin effect
    • Machado J.A.T., Galhano A.M. Fractional order inductive phenomena based on the skin effect. Nonlinear Dyn 2012, 68(1-2):107-115.
    • (2012) Nonlinear Dyn , vol.68 , Issue.1-2 , pp. 107-115
    • Machado, J.A.T.1    Galhano, A.M.2
  • 34
    • 0032613548 scopus 로고    scopus 로고
    • Applicability of distribution functions for the Havriliak-Negami spectral function
    • Zorn R. Applicability of distribution functions for the Havriliak-Negami spectral function. J Polym Sci Part B: Polym Phys 1999, 37(10):1043-1044.
    • (1999) J Polym Sci Part B: Polym Phys , vol.37 , Issue.10 , pp. 1043-1044
    • Zorn, R.1
  • 35
    • 0037154565 scopus 로고    scopus 로고
    • Logarithmic moments of relaxation time distributions
    • Zorn R. Logarithmic moments of relaxation time distributions. J Chem Phys 2002, 116(8):3204-3209.
    • (2002) J Chem Phys , vol.116 , Issue.8 , pp. 3204-3209
    • Zorn, R.1
  • 36
    • 41349085322 scopus 로고    scopus 로고
    • H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems
    • Hilfer R. H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems. Phys Rev E 2002, 65(6):061510.
    • (2002) Phys Rev E , vol.65 , Issue.6 , pp. 061510
    • Hilfer, R.1
  • 37
    • 79953685491 scopus 로고    scopus 로고
    • Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
    • de Oliveira J.V.J.E., Mainardi F. Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur Phys J 2011, 193(1):161-171.
    • (2011) Eur Phys J , vol.193 , Issue.1 , pp. 161-171
    • de Oliveira, J.V.J.E.1    Mainardi, F.2
  • 38
    • 84905881342 scopus 로고    scopus 로고
    • On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
    • Mainardi F, Garrappa R. On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics. J Comput Phys; doi:. doi:10.1016/j.jcp.2014.08.006.
    • J Comput Phys
    • Mainardi, F.1    Garrappa, R.2
  • 40
    • 84896939823 scopus 로고    scopus 로고
    • Some pioneers of the applications of fractional calculus
    • Valério D., Machado J.T., Kiryakova V. Some pioneers of the applications of fractional calculus. Frac Calc Appl Anal 2014, 17(2):552-578.
    • (2014) Frac Calc Appl Anal , vol.17 , Issue.2 , pp. 552-578
    • Valério, D.1    Machado, J.T.2    Kiryakova, V.3
  • 41
    • 0031543193 scopus 로고    scopus 로고
    • Cole-Davidson dielectric relaxation as a self-similar relaxation process
    • Nigmatullin R., Ryabov Y.E. Cole-Davidson dielectric relaxation as a self-similar relaxation process. Phys Solid State 1997, 39(1):87-90.
    • (1997) Phys Solid State , vol.39 , Issue.1 , pp. 87-90
    • Nigmatullin, R.1    Ryabov, Y.E.2
  • 42
    • 21544434903 scopus 로고    scopus 로고
    • Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon
    • Jeon T.-I., Grischkowsky D. Observation of a Cole-Davidson type complex conductivity in the limit of very low carrier densities in doped silicon. Appl Phys Lett 1998, 72(18):2259-2261.
    • (1998) Appl Phys Lett , vol.72 , Issue.18 , pp. 2259-2261
    • Jeon, T.-I.1    Grischkowsky, D.2
  • 43
    • 1642567420 scopus 로고    scopus 로고
    • A physical hypothesis for Cole-Davidson behavior
    • Calderwood J. A physical hypothesis for Cole-Davidson behavior. IEEE Trans Dielectr Electr Insul 2004, 10(6):1006-1011.
    • (2004) IEEE Trans Dielectr Electr Insul , vol.10 , Issue.6 , pp. 1006-1011
    • Calderwood, J.1
  • 44
    • 20444386984 scopus 로고    scopus 로고
    • Fractional hydrodynamic equations for fractal media
    • Tarasov V.E. Fractional hydrodynamic equations for fractal media. Ann Phys 2005, 318(2):286-307.
    • (2005) Ann Phys , vol.318 , Issue.2 , pp. 286-307
    • Tarasov, V.E.1
  • 45
    • 33745698038 scopus 로고    scopus 로고
    • Fractional system identification for lead acid battery state of charge estimation
    • Sabatier J., Aoun M., Oustaloup A., Grégoire G., Ragot F., Roy P. Fractional system identification for lead acid battery state of charge estimation. Signal Process 2006, 86(10):2645-2657.
    • (2006) Signal Process , vol.86 , Issue.10 , pp. 2645-2657
    • Sabatier, J.1    Aoun, M.2    Oustaloup, A.3    Grégoire, G.4    Ragot, F.5    Roy, P.6
  • 47
    • 84873663209 scopus 로고    scopus 로고
    • Description of the anomalous dielectric relaxation in disordered systems in the frame of the Mori-Zwanzig formalism
    • Khamzin A., Nigmatullin R., Popov I. Description of the anomalous dielectric relaxation in disordered systems in the frame of the Mori-Zwanzig formalism. J Phys Conf Ser 2012, 394(1):012013.
    • (2012) J Phys Conf Ser , vol.394 , Issue.1 , pp. 012013
    • Khamzin, A.1    Nigmatullin, R.2    Popov, I.3
  • 48
    • 84884228204 scopus 로고    scopus 로고
    • An enhanced fractional order model of ionic polymer-metal composites actuator
    • (Article ID 717659)
    • Caponetto R., Graziani S., Sapuppo F., Tomasello V. An enhanced fractional order model of ionic polymer-metal composites actuator. Adv Math Phys 2013, 2013:6. (Article ID 717659).
    • (2013) Adv Math Phys , vol.2013 , pp. 6
    • Caponetto, R.1    Graziani, S.2    Sapuppo, F.3    Tomasello, V.4
  • 50
    • 0015127532 scopus 로고
    • Memristor - the missing circuit element
    • Chua L.O. Memristor - the missing circuit element. IEEE Trans Circuit Theory 1971, 18(2):507-519.
    • (1971) IEEE Trans Circuit Theory , vol.18 , Issue.2 , pp. 507-519
    • Chua, L.O.1
  • 51
    • 0019079281 scopus 로고
    • Device modeling via basic nonlinear circuits elements
    • Chua L.O., Kang S.M. Device modeling via basic nonlinear circuits elements. IEEE Trans Circuits Systems 1980, 27(11):1014-1044.
    • (1980) IEEE Trans Circuits Systems , vol.27 , Issue.11 , pp. 1014-1044
    • Chua, L.O.1    Kang, S.M.2
  • 53
    • 84861189029 scopus 로고    scopus 로고
    • Port-hamiltonian formulation of systems with memory
    • Jeltsema D., Dòria-Cerezo A. Port-hamiltonian formulation of systems with memory. Proc IEEE 2012, 100(6):1928-1937.
    • (2012) Proc IEEE , vol.100 , Issue.6 , pp. 1928-1937
    • Jeltsema, D.1    Dòria-Cerezo, A.2
  • 54
    • 84865973843 scopus 로고    scopus 로고
    • Fractional generalization of memristor and higher order elements
    • Machado J.A.T. Fractional generalization of memristor and higher order elements. Commun Nonlinear Sci Numer Simul 2013, 18(12):264-275.
    • (2013) Commun Nonlinear Sci Numer Simul , vol.18 , Issue.12 , pp. 264-275
    • Machado, J.A.T.1
  • 55
    • 70349395653 scopus 로고
    • Extension of the formula for the nth power of a square matrix to negative and fractional values of n
    • Astin J. Extension of the formula for the nth power of a square matrix to negative and fractional values of n. Math Gaz 1967, 51(377):228-232.
    • (1967) Math Gaz , vol.51 , Issue.377 , pp. 228-232
    • Astin, J.1
  • 56
    • 84877317574 scopus 로고
    • On fractional powers of a matrix
    • Waugh F.V., Abel M.E. On fractional powers of a matrix. J Amer Statist Assoc 1967, 62(319):1018-1021.
    • (1967) J Amer Statist Assoc , vol.62 , Issue.319 , pp. 1018-1021
    • Waugh, F.V.1    Abel, M.E.2
  • 57
    • 84924751240 scopus 로고
    • Binomial theorem applications in matrix fractional powers calculation
    • Arias A., Gutiérrez E., Pozo E. Binomial theorem applications in matrix fractional powers calculation. Period Polytech Transp Eng 1990, 18(1-2):75-79.
    • (1990) Period Polytech Transp Eng , vol.18 , Issue.1-2 , pp. 75-79
    • Arias, A.1    Gutiérrez, E.2    Pozo, E.3
  • 58
    • 17544381599 scopus 로고    scopus 로고
    • Algorithms for the matrix pth root
    • Bini D.A., Higham N.J., Meini B. Algorithms for the matrix pth root. Numer Algorithms 2005, 39(4):349-378.
    • (2005) Numer Algorithms , vol.39 , Issue.4 , pp. 349-378
    • Bini, D.A.1    Higham, N.J.2    Meini, B.3


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