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Volumn 91, Issue 3, 2011, Pages 350-371

On the fractional signals and systems

Author keywords

Caputo; Fractional derivative; Fractional linear systems; Grunwald Letnikov derivative; Riemann Liouville

Indexed keywords

CAPUTO; FRACTIONAL DERIVATIVE; FRACTIONAL LINEAR SYSTEMS; GRUNWALD-LETNIKOV DERIVATIVE; RIEMANN-LIOUVILLE;

EID: 78049325210     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2010.08.003     Document Type: Review
Times cited : (255)

References (179)
  • 32
    • 15544372486 scopus 로고    scopus 로고
    • Special issue on fractional derivatives and their applications
    • O.P. Agrawal, J.A.T. Machado, J. Sabatier (Eds.) December
    • O.P. Agrawal, J.A.T. Machado, J. Sabatier (Eds.), Special issue on fractional derivatives and their applications, Nonlinear Dynamics 38(14) (2004) December.
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4
  • 33
    • 33846527655 scopus 로고    scopus 로고
    • Special issue on fractional order calculus and its applications
    • J.A.T. Machado (Ed.) July
    • J.A.T. Machado (Ed.), Special issue on fractional order calculus and its applications, Nonlinear Dynamics 29 (14) (2002) July.
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4
  • 34
    • 77952818738 scopus 로고    scopus 로고
    • Special issue on fractional signal processing and applications
    • M.D. Ortigueira, J.A.T. Machado (Eds.) November
    • M.D. Ortigueira, J.A.T. Machado (Eds.), Special issue on fractional signal processing and applications, Signal Processing 83 (11) (2003) November.
    • (2003) Signal Processing , vol.83 , Issue.11
  • 35
    • 33745967716 scopus 로고    scopus 로고
    • Special section: Fractional calculus applications in signals and systems
    • M.D. Ortigueira, J.A.T. Machado (Eds.) October
    • M.D. Ortigueira, J.A.T. Machado (Eds.), Special section: fractional calculus applications in signals and systems, Signal Processing 86 (10) (2006) October.
    • (2006) Signal Processing , vol.86 , Issue.10
  • 37
    • 55549103342 scopus 로고    scopus 로고
    • Approximate analytical solution to fractional modified kdv equations
    • O. Abdulaziz, I. Hashim, E.S. Ismail, Approximate analytical solution to fractional modified kdv equations, Mathematical and Computer Modelling, 49 (12) (2009) 136145.
    • (2009) Mathematical and Computer Modelling , vol.49 , Issue.1-2 , pp. 136-145
    • Abdulaziz, O.1    Hashim, I.2    Ismail, E.S.3
  • 38
    • 37549050173 scopus 로고    scopus 로고
    • Solving systems of fractional differential equations by homotopyperturbation method
    • O. Abdulaziz, I. Hashim, and S. Momani Solving systems of fractional differential equations by homotopyperturbation method Physics Letters A 372 2008 451 459
    • (2008) Physics Letters A , vol.372 , pp. 451-459
    • Abdulaziz, O.1    Hashim, I.2    Momani, S.3
  • 40
    • 0027545685 scopus 로고
    • Novel digital integrator and differentiator
    • M.A. Al-Alaoui, Novel digital integrator and differentiator, Electronics Letters 29(4) (1993) 376378.
    • (1993) Electronics Letters , vol.29 , Issue.4 , pp. 376-378
    • Al-Alaoui, M.A.1
  • 41
    • 0028696254 scopus 로고
    • The fractional-order dynamics of brainstem vestibulo-ocular dynamics of brainstem vestibularoculomotor neurons
    • T.J. Anastasio The fractional-order dynamics of brainstem vestibulo-ocular dynamics of brainstem vestibularoculomotor neurons Biological Cybernetics 72 1994 69 79
    • (1994) Biological Cybernetics , vol.72 , pp. 69-79
    • Anastasio, T.J.1
  • 42
    • 0032201202 scopus 로고    scopus 로고
    • Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior
    • T.J. Anastasio Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior Biological Cybernetics 79 1998 377 391
    • (1998) Biological Cybernetics , vol.79 , pp. 377-391
    • Anastasio, T.J.1
  • 43
    • 0012820367 scopus 로고
    • Solution of non-integer order differential equations via the adomian decomposition method
    • H.L. Arora, and F.I. Abdelwahid Solution of non-integer order differential equations via the adomian decomposition method Applied Mathematics Letters 6 1 1993 21 23
    • (1993) Applied Mathematics Letters , vol.6 , Issue.1 , pp. 21-23
    • Arora, H.L.1    Abdelwahid, F.I.2
  • 45
    • 79960746097 scopus 로고    scopus 로고
    • Pole-zero approximations of digital fractional-order integrators and differentiators using signal modeling techniques
    • July Prague, Czech Republic
    • R.S. Barbosa, J.A.T. Machado, I.M. Ferreira, Pole-zero approximations of digital fractional-order integrators and differentiators using signal modeling techniques, in: Proceedings of the 16th IFAC World Congress, July 2005, Prague, Czech Republic.
    • (2005) Proceedings of the 16th IFAC World Congress
    • Barbosa, R.S.1    MacHado, J.A.T.2    Ferreira, I.M.3
  • 46
    • 84981825145 scopus 로고
    • Definition of physically consistent damping laws with fractional derivatives
    • H. Beyer, and S. Kempfle Definition of physically consistent damping laws with fractional derivatives Zeitschrift fur Angewandte Mathematik und Mechanik 75 1995 623 635
    • (1995) Zeitschrift fur Angewandte Mathematik und Mechanik , vol.75 , pp. 623-635
    • Beyer, H.1    Kempfle, S.2
  • 47
    • 0003369375 scopus 로고    scopus 로고
    • Numerical treatment of differential equations of fractional order
    • L. Blank, Numerical treatment of differential equations of fractional order, Numerical Analysis Report 287, 1996.
    • (1996) Numerical Analysis Report , vol.287
    • Blank, L.1
  • 48
    • 32644457439 scopus 로고    scopus 로고
    • The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations
    • N. Bildik, and A. Konuralp The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations International Journal of Nonlinear Science and Numerical Simulations 7 1 2006 65 70 (Pubitemid 43246582)
    • (2006) International Journal of Nonlinear Sciences and Numerical Simulation , vol.7 , Issue.1 , pp. 65-70
    • Bildik, N.1    Konuralp, A.2
  • 53
    • 34247394106 scopus 로고    scopus 로고
    • On systems of linear fractional differential equations with constant coefficients
    • B. Bonilla, M. Rivero, and J.J. Trujillo On systems of linear fractional differential equations with constant coefficients Applied Mathematics and Computation 187 9 2007 68 78
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.9 , pp. 68-78
    • Bonilla, B.1    Rivero, M.2    Trujillo, J.J.3
  • 54
    • 34247323827 scopus 로고    scopus 로고
    • Fractional differential equations as alternative models to nonlinear differential equations
    • DOI 10.1016/j.amc.2006.08.105, PII S0096300306011398
    • B. Bonilla, M. Rivero, L. Rodrguez-Germ, and J.J. Trujillo Fractional differential equations as alternative models to the nonlinear fractional differential equations Applied Mathematics and Computation 187 9 2007 79 88 (Pubitemid 46635706)
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.1 SPEC. ISS. , pp. 79-88
    • Bonilla, B.1    Rivero, M.2    Rodriguez-Germa, L.3    Trujillo, J.J.4
  • 56
    • 0004225568 scopus 로고
    • On a concept of derivative of complex order with applications to special functions
    • L.M.C. Campos On a concept of derivative of complex order with applications to special functions IMA Journal of Applied Mathematics 33 1984 109 133
    • (1984) IMA Journal of Applied Mathematics , vol.33 , pp. 109-133
    • Campos, L.M.C.1
  • 57
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent, Part II
    • M. Caputo Linear models of dissipation whose Q is almost frequency independent, Part II Geophysical Journal of the Royal Astronomical Society 13 1967 529 539
    • (1967) Geophysical Journal of the Royal Astronomical Society , vol.13 , pp. 529-539
    • Caputo, M.1
  • 59
    • 0141961689 scopus 로고    scopus 로고
    • A new IIR-type digital fractional order differentiator
    • Y.Q. Chen, and B.M. Vinagre A new IIR-type digital fractional order differentiator Signal Processing 83 11 2003 2359 2365
    • (2003) Signal Processing , vol.83 , Issue.11 , pp. 2359-2365
    • Chen, Y.Q.1    Vinagre, B.M.2
  • 60
    • 15544372160 scopus 로고    scopus 로고
    • Continued fraction expansion approaches to discretizing fractional order derivativesan expository review
    • Y.Q. Chen, B.M. Vinagre, and I. Podlubny Continued fraction expansion approaches to discretizing fractional order derivativesan expository review Nonlinear Dynamics 38 2004 155 170
    • (2004) Nonlinear Dynamics , vol.38 , pp. 155-170
    • Chen, Y.Q.1    Vinagre, B.M.2    Podlubny, I.3
  • 61
  • 63
    • 37149033452 scopus 로고    scopus 로고
    • A fractional derivative model to describe arterial viscoelasticity
    • D. Craiem, and R.L. Armentano A fractional derivative model to describe arterial viscoelasticity Biorheology 44 2007 251 263
    • (2007) Biorheology , vol.44 , pp. 251-263
    • Craiem, D.1    Armentano, R.L.2
  • 64
    • 10344238128 scopus 로고    scopus 로고
    • Adomian decomposition: A tool for solving a system of fractional differential equations
    • DOI 10.1016/j.jmaa.2004.07.039, PII S0022247X04006286
    • V. Daftardar-Gejji, and H. Jafari Adomian decomposition: a tool for solving a system of fractional differential equations Journal of Mathematical Analysis and Applications 301 2 2005 508 518 (Pubitemid 39630973)
    • (2005) Journal of Mathematical Analysis and Applications , vol.301 , Issue.2 , pp. 508-518
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 66
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • K. Diethelm An algorithm for the numerical solution of differential equations of fractional order Electronic Transactions on Numerical Analysis 5 1997 1 6 (Pubitemid 38870919)
    • (1997) Electronic Transactions on Numerical Analysis , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 67
    • 0031477557 scopus 로고    scopus 로고
    • Generalized compound quadrature formulae for finite-part integrals
    • K. Diethelm Generalized compound quadrature formulae for finite-part integrals IMA Journal of Numerical Analysis 17 3 1997 479 493
    • (1997) IMA Journal of Numerical Analysis , vol.17 , Issue.3 , pp. 479-493
    • Diethelm, K.1
  • 69
    • 0012899160 scopus 로고    scopus 로고
    • Numerical solution of the BagleyTorvik equation
    • K. Diethelm, and N.J. Ford Numerical solution of the BagleyTorvik equation BIT 42 3 2002 490 507
    • (2002) BIT , vol.42 , Issue.3 , pp. 490-507
    • Diethelm, K.1    Ford, N.J.2
  • 70
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • K. Diethelm, N.J. Ford, and A.D. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 2002 3 22
    • (2002) Nonlinear Dynamics , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 73
    • 0043044718 scopus 로고    scopus 로고
    • Numerical solution of fractional order differential equations by extrapolation
    • K. Diethelm, and G. Walz Numerical solution for fractional differential equations by extrapolation Numerical Algorithms 16 1997 231 253 (Pubitemid 127429647)
    • (1997) Numerical Algorithms , vol.16 , Issue.3-4 , pp. 231-253
    • Diethelm, K.1    Walz, G.2
  • 75
    • 34548745993 scopus 로고    scopus 로고
    • Fractional paradigm in electromagnetic theory
    • N. Engheta Fractional paradigm in electromagnetic theory D.H. Werner, R. Mittra, Frontiers in Electromagnetics 2000 IEEE Press (Chapter 12)
    • (2000) Frontiers in Electromagnetics
    • Engheta, N.1
  • 76
    • 0000824896 scopus 로고    scopus 로고
    • Modal synthesis when modeling damping by use of fractional derivatives
    • A. Fenander Modal synthesis when modeling damping by use of fractional derivatives American Institute of Aeronautics and Astronautics Journal 34 5 1996 1051 1058
    • (1996) American Institute of Aeronautics and Astronautics Journal , vol.34 , Issue.5 , pp. 1051-1058
    • Fenander, A.1
  • 78
    • 17444419514 scopus 로고
    • The adomian method applied to some extraordinary differential equations
    • A.J. George, and A. Chakrabarti The adomian method applied to some extraordinary differential equations Applied Mathematics Letters 8 3 1995 91 97
    • (1995) Applied Mathematics Letters , vol.8 , Issue.3 , pp. 91-97
    • George, A.J.1    Chakrabarti, A.2
  • 79
    • 0141974618 scopus 로고    scopus 로고
    • Fractional diffusion processes: Probability distributions and continuous time random walk
    • R. Gorenflo, and F. Mainardi Fractional diffusion processes: probability distributions and continuous time random walk G. Rangarajan, M. Ding, Long Range Dependent Processes: Theory and Applications 2003 Springer-Verlag
    • (2003) Long Range Dependent Processes: Theory and Applications
    • Gorenflo, R.1    Mainardi, F.2
  • 80
    • 0036650850 scopus 로고    scopus 로고
    • Time-fractional diffusion: A discrete random walk approach
    • R. Gorenflo, F. Mainardi, D. Moretti, and P. Paradisi Time-fractional diffusion: a discrete random walk approach Nonlinear Dynamics 29 14 2002 129 143
    • (2002) Nonlinear Dynamics , vol.29 , Issue.14 , pp. 129-143
    • Gorenflo, R.1    Mainardi, F.2    Moretti, D.3    Paradisi, P.4
  • 84
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for non-linear problems
    • J.H. He A coupling method of a homotopy technique and a perturbation technique for non-linear problems International Journal of Non-Linear Mechanics 35 1 2000 37 43
    • (2000) International Journal of Non-Linear Mechanics , vol.35 , Issue.1 , pp. 37-43
    • He, J.H.1
  • 85
    • 33845888181 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives
    • N. Heymans, and I. Podlubny Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives Rheol Acta 37 2005 1 7
    • (2005) Rheol Acta , vol.37 , pp. 1-7
    • Heymans, N.1    Podlubny, I.2
  • 86
    • 19944370478 scopus 로고    scopus 로고
    • The fundamental solution of the spacetime fractional advectiondispersion equation
    • F. Huang, and F. Liu The fundamental solution of the spacetime fractional advectiondispersion equation Journal of Applied Mathematics and Computing 18 2 2005 339 350
    • (2005) Journal of Applied Mathematics and Computing , vol.18 , Issue.2 , pp. 339-350
    • Huang, F.1    Liu, F.2
  • 87
    • 33747286487 scopus 로고    scopus 로고
    • The time-fractional diffusion equation and fractional advectiondispersion equation
    • F. Huang, and F. Liu The time-fractional diffusion equation and fractional advectiondispersion equation ANZIAM Journal 46 2005 1 14
    • (2005) ANZIAM Journal , vol.46 , pp. 1-14
    • Huang, F.1    Liu, F.2
  • 88
    • 0036295450 scopus 로고    scopus 로고
    • Deviations of capacitive and indutive loops in the electrochemical impedance of a dissolving iron electrode
    • M. Itagaki, A. Taya, K. Watanabe, and K. Noda Deviations of capacitive and indutive loops in the electrochemical impedance of a dissolving iron electrode Analytical Sciences 18 6 2002 641 644
    • (2002) Analytical Sciences , vol.18 , Issue.6 , pp. 641-644
    • Itagaki, M.1    Taya, A.2    Watanabe, K.3    Noda, K.4
  • 89
    • 33746218471 scopus 로고    scopus 로고
    • Solving a system of nonlinear fractional differential equations using Adomian decomposition
    • DOI 10.1016/j.cam.2005.10.017, PII S0377042705006278
    • H. Jafari, and V. Daftardar-Gejji Solving a system of nonlinear fractional differential equations using Adomian decomposition Journal of Computational and Applied Mathematics 196 2 2006 644 651 (Pubitemid 44093887)
    • (2006) Journal of Computational and Applied Mathematics , vol.196 , Issue.2 , pp. 644-651
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 91
    • 0020102486 scopus 로고
    • 1/f noise
    • March
    • M.S. Keshner, 1/f noise, in: Proceedings of IEEE, vol. 70, no. 3, March 1982, pp. 212218.
    • (1982) Proceedings of IEEE , vol.70 , Issue.3 , pp. 212-218
    • Keshner, M.S.1
  • 92
    • 34247380622 scopus 로고    scopus 로고
    • α-Analytic solutions of some linear fractional differential equations with variable coefficients
    • DOI 10.1016/j.amc.2006.08.121, PII S0096300306011581
    • A.A. Kilbas, M. Rivero, L. Rodrguez-Germ, and J.J. Trujillo α-analytic solutions of some linear fractional differential equations with variable coefficients Applied Mathematics and Computation 187 9 2007 239 249 (Pubitemid 46635723)
    • (2007) Applied Mathematics and Computation , vol.187 , Issue.1 SPEC. ISS. , pp. 239-249
    • Kilbas, A.A.1    Rivero, M.2    Rodriguez-Germa, L.3    Trujillo, J.J.4
  • 94
    • 84880143457 scopus 로고    scopus 로고
    • Characterization of a fractional order element realized by dipping a capacitive type probe in polarizable medium
    • Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Caparica, Portugal, November 4-6
    • M.S., Krishna, S., Das, K. Biswas, B. Goswami, Characterization of a fractional order element realized by dipping a capacitive type probe in polarizable medium, in: Proceedings of the Symposium on Fractional Signals and Systems, Lisbon'09, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Caparica, Portugal, November 46.
    • Proceedings of the Symposium on Fractional Signals and Systems, Lisbon'09
    • Krishna, S.M.1    Das, S.2    Biswas, K.3    Goswami, B.4
  • 95
    • 33745712076 scopus 로고    scopus 로고
    • An approximate method for numerical solution of fractional differential equations
    • P. Kumar, and O.P. Agrawal. An approximate method for numerical solution of fractional differential equations Signal Processing 86 2006 2602 2610
    • (2006) Signal Processing , vol.86 , pp. 2602-2610
    • Kumar, P.1    Agrawal, O.P.2
  • 98
    • 0000449295 scopus 로고
    • On the stability of linear multistep methods for Volterra convolution equations
    • C. Lubich On the stability of linear multistep methods for Volterra convolution equations IMA Journal of Numerical Analysis 3 4 1983 439 465
    • (1983) IMA Journal of Numerical Analysis , vol.3 , Issue.4 , pp. 439-465
    • Lubich, C.1
  • 99
    • 84966227123 scopus 로고
    • Fractional linear multistep methods for AbelVolterra integral equations of the second kind
    • C. Lubich Fractional linear multistep methods for AbelVolterra integral equations of the second kind Mathematics of Computation 45 172 1985 463 469
    • (1985) Mathematics of Computation , vol.45 , Issue.172 , pp. 463-469
    • Lubich, C.1
  • 103
    • 0034325075 scopus 로고    scopus 로고
    • Measurement and modelling of high-power performance of carbon-based supercapacitors
    • P.J. Mahon, G.L. Paul, S.M. Kesshishian, and A.M. Vassallo Measurement and modelling of high-power performance of carbon-based supercapacitors Journal of Power Sources 91 1 2000 68 76
    • (2000) Journal of Power Sources , vol.91 , Issue.1 , pp. 68-76
    • Mahon, P.J.1    Paul, G.L.2    Kesshishian, S.M.3    Vassallo, A.M.4
  • 105
    • 0029427754 scopus 로고
    • The time fractional diffusion-wave equation
    • F. Mainardi The time fractional diffusion-wave equation Radiophysics and Quantum Electronics 38 12 1995 13 24
    • (1995) Radiophysics and Quantum Electronics , vol.38 , Issue.12 , pp. 13-24
    • Mainardi, F.1
  • 106
    • 0026219915 scopus 로고
    • Fractional-derivative maxwell model for viscous dampers
    • N. Makris, and M.C. Constantinou Fractional-derivative maxwell model for viscous dampers Journal of Structural Engineering 117 9 1991 2708 2724
    • (1991) Journal of Structural Engineering , vol.117 , Issue.9 , pp. 2708-2724
    • Makris, N.1    Constantinou, M.C.2
  • 107
    • 0000501589 scopus 로고
    • The fractional brownian motions, fractional noises and applications
    • B.B. Mandelbrot, and J.W. Van Ness The fractional brownian motions, fractional noises and applications SIAM Review 10 4 1968 422 437
    • (1968) SIAM Review , vol.10 , Issue.4 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 109
    • 24144494623 scopus 로고    scopus 로고
    • An explicit and numerical solutions of the fractional KdV equation
    • S. Momani An explicit and numerical solutions of the fractional KdV equation Mathematics and Computers in Simulation 70 2 2005 110 118
    • (2005) Mathematics and Computers in Simulation , vol.70 , Issue.2 , pp. 110-118
    • Momani, S.1
  • 110
    • 78049337482 scopus 로고    scopus 로고
    • Numerical simulation of a dynamic system containing fractional derivatives
    • Shanghai, China
    • S. Momani, Numerical simulation of a dynamic system containing fractional derivatives, in: International Symposium on Nonlinear Dynamics, Shanghai, China, 2005.
    • (2005) International Symposium on Nonlinear Dynamics
    • Momani, S.1
  • 111
    • 33750901303 scopus 로고    scopus 로고
    • A numerical scheme for the solution of multi-order fractional differential equations
    • S. Momani A numerical scheme for the solution of multi-order fractional differential equations Applied Mathematics and Computation 182 1 2006 761 770
    • (2006) Applied Mathematics and Computation , vol.182 , Issue.1 , pp. 761-770
    • Momani, S.1
  • 112
    • 24944474278 scopus 로고    scopus 로고
    • Application of He's variational iteration method to Helmholtz equation
    • S. Momani, and S. Abuasad Application of He's variational iteration method to Helmholtz equation Chaos, Solitons & Fractals 27 5 2006 1119 1123
    • (2006) Chaos, Solitons & Fractals , vol.27 , Issue.5 , pp. 1119-1123
    • Momani, S.1    Abuasad, S.2
  • 113
    • 12244291039 scopus 로고    scopus 로고
    • Numerical solutions for systems of fractional differential equations by the decomposition method
    • S. Momani, and K. Al-Khaled Numerical solutions for systems of fractional differential equations by the decomposition method Applied Mathematics and Computation 162 3 2005 1351 1365
    • (2005) Applied Mathematics and Computation , vol.162 , Issue.3 , pp. 1351-1365
    • Momani, S.1    Al-Khaled, K.2
  • 114
    • 34748865972 scopus 로고    scopus 로고
    • Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
    • S. Momani, and Z. Odibat Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations Computers and Mathematics with Applications 54 78 2007 910 919
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.78 , pp. 910-919
    • Momani, S.1    Odibat, Z.2
  • 115
    • 34247395044 scopus 로고    scopus 로고
    • Homotopy perturbation method for nonlinear partial differential equations of fractional order
    • S. Momani, and Z. Odibat Homotopy perturbation method for nonlinear partial differential equations of fractional order Physics Letters A 365 56 2007 345 350
    • (2007) Physics Letters A , vol.365 , Issue.56 , pp. 345-350
    • Momani, S.1    Odibat, Z.2
  • 117
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • S. Momani, and Z. Odibat Numerical comparison of methods for solving linear differential equations of fractional order Chaos, Solitons & Fractals 31 2007 1248 1255
    • (2007) Chaos, Solitons & Fractals , vol.31 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 118
    • 33750457322 scopus 로고    scopus 로고
    • An efficient method for solving systems of fractional integro-differential equations
    • DOI 10.1016/j.camwa.2006.02.011, PII S0898122106002124
    • S. Momani, and R. Qaralleh An efficient method for solving systems of fractional integro-differential equations Computers and Mathematics with Applications 52 3-4 2006 459 470 (Pubitemid 44648715)
    • (2006) Computers and Mathematics with Applications , vol.52 , Issue.3-4 , pp. 459-470
    • Momani, S.1    Qaralleh, R.2
  • 119
    • 51449124394 scopus 로고    scopus 로고
    • Some experiences in linear and nonlinear fractional order control
    • Industrial Engineering School (University of Extremadura), 15-17 October Badajoz, Spain
    • C.A. Monje, B.M. Vinagre, A.J. Caldern, J.I. Surez, I. Tejado, Some experiences in linear and nonlinear fractional order control, Presentation at the Symposium on Applied Fractional Calculus (SAFC07), Industrial Engineering School (University of Extremadura), 1517 October 2007, Badajoz, Spain.
    • (2007) Presentation at the Symposium on Applied Fractional Calculus (SAFC07)
    • Monje, C.A.1
  • 122
    • 0033899008 scopus 로고    scopus 로고
    • Introduction to fractional signal processing, part 2: Discrete-time systems
    • M.D. Ortigueira Introduction to fractional signal processing, part 2: discrete-time systems IEE Proceedings on Vision, Image and Signal Processing 147 1 2000 71 78
    • (2000) IEE Proceedings on Vision, Image and Signal Processing , vol.147 , Issue.1 , pp. 71-78
    • Ortigueira, M.D.1
  • 123
    • 0142010055 scopus 로고    scopus 로고
    • On the initial conditions in continuous-time fractional linear systems
    • M.D. Ortigueira On the initial conditions in continuous-time fractional linear systems Signal Processing 83 11 2003 2301 2309
    • (2003) Signal Processing , vol.83 , Issue.11 , pp. 2301-2309
    • Ortigueira, M.D.1
  • 129
    • 33846257141 scopus 로고    scopus 로고
    • Pseudo-fractional ARMA modelling using a double Levinson recursion
    • M.D. Ortigueira, and A.J. Serralheiro Pseudo-fractional ARMA modelling using a double Levinson recursion IET Control Theory and Applications 1 1 2007 173 178
    • (2007) IET Control Theory and Applications , vol.1 , Issue.1 , pp. 173-178
    • Ortigueira, M.D.1    Serralheiro, A.J.2
  • 130
    • 38749093369 scopus 로고    scopus 로고
    • On the relation between the fractional Brownian motion and the fractional derivatives
    • M.D. Ortigueira, and A.G. Batista On the relation between the fractional Brownian motion and the fractional derivatives Physics Letters A 372 7 2008 958 968
    • (2008) Physics Letters A , vol.372 , Issue.7 , pp. 958-968
    • Ortigueira, M.D.1    Batista, A.G.2
  • 131
    • 78049332707 scopus 로고    scopus 로고
    • The initial conditions of Riemann-Liouville and Caputo derivatives
    • June 30-July 4 Saint Petersburg, Russia
    • M.D. Ortigueira, F.V. Coito, The initial conditions of RiemannLiouville and Caputo derivatives, in: Proceedings of the Sixth EUROMECH Conference ENOC 2008, June 30July 4, 2008, Saint Petersburg, Russia.
    • (2008) Proceedings of the Sixth EUROMECH Conference ENOC 2008
    • Ortigueira, M.D.1    Coito, F.V.2
  • 134
    • 0019623026 scopus 로고
    • Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation
    • A. Oustaloup Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation IEEE Transactions on Circuits and Systems CAS-28 10 1981
    • (1981) IEEE Transactions on Circuits and Systems , vol.28 , Issue.10
    • Oustaloup, A.1
  • 135
    • 85019485305 scopus 로고
    • The CRONE control of resonant plants: Application to a flexible transmission
    • A. Oustaloup, B. Mathieu, and P. Lanusse The CRONE control of resonant plants: application to a flexible transmission European Journal of Control 1 2 1995 113 121
    • (1995) European Journal of Control , vol.1 , Issue.2 , pp. 113-121
    • Oustaloup, A.1    Mathieu, B.2    Lanusse, P.3
  • 138
    • 0001082337 scopus 로고    scopus 로고
    • The electrode-tissue interface in living heart: Equivalent circuit as a function of surface area
    • M. Ovadia, and D.H. Zavitz The electrode-tissue interface in living heart: equivalent circuit as a function of surface area Electroanalysis 10 1998 262 272
    • (1998) Electroanalysis , vol.10 , pp. 262-272
    • Ovadia, M.1    Zavitz, D.H.2
  • 139
    • 78049345257 scopus 로고    scopus 로고
    • 17 October 2005 (Updated 25 March 2009)
    • I. Podlubny, M. Kacenak, Mittag-Leffler function, 〈 http://www.mathworks.com/matlabcentral/fileexchange/8738 〉, 17 October 2005 (Updated 25 March 2009).
    • Mittag-Leffler Function
    • Podlubny, I.1    Kacenak, M.2
  • 140
    • 77949900646 scopus 로고    scopus 로고
    • Matrix approach to discretization of fractional derivatives and to solution of fractional differential equations and their systems
    • September 22-25, Palma de Mallorca, Spain, doi: 10.1109/ETFA.2009.5347166
    • I. Podlubny, T. Skovranek, B. Vinagre, Matrix approach to discretization of fractional derivatives and to solution of fractional differential equations and their systems, in IEEE Conference on Emerging Technologies Factory Automation ETFA 2009, September 2225, Palma de Mallorca, Spain, doi: 10.1109/ETFA.2009.5347166, 2009.
    • (2009) IEEE Conference on Emerging Technologies Factory Automation ETFA 2009
    • Podlubny, I.1    Skovranek, T.2    Vinagre, B.3
  • 141
    • 33744801528 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus
    • I. Podlubny Matrix approach to discrete fractional calculus Fractional Calculus and Applied Analysis 3 4 2000 359 386
    • (2000) Fractional Calculus and Applied Analysis , vol.3 , Issue.4 , pp. 359-386
    • Podlubny, I.1
  • 142
    • 0022043660 scopus 로고
    • Cascade realization of the irrational immittance S1/2
    • April
    • V. Ramachandran, C.S. Cargour, M. Ahmadi, Cascade realization of the irrational immittance S1/2, in: IEE Proceedings, Part G, vol. 132, no. 2, April 1985, pp. 6467.
    • (1985) IEE Proceedings, Part G , vol.132 , Issue.2 , pp. 64-67
    • Ramachandran, V.1    Cargour, C.S.2    Ahmadi, M.3
  • 143
    • 24944478244 scopus 로고    scopus 로고
    • An approximate solution of a nonlinear fractional differential equation by adomian decomposition method
    • S.S. Ray, and R.K. Bera An approximate solution of a nonlinear fractional differential equation by adomian decomposition method Applied Mathematics and Computation 167 1 2005 561 571
    • (2005) Applied Mathematics and Computation , vol.167 , Issue.1 , pp. 561-571
    • Ray, S.S.1    Bera, R.K.2
  • 144
    • 17444386836 scopus 로고    scopus 로고
    • Solution of an extraordinary differential equation by adomian decomposition method
    • S.S. Ray, and R.K. Bera Solution of an extraordinary differential equation by adomian decomposition method Journal of Applied Mathematics 4 2004 331 338
    • (2004) Journal of Applied Mathematics , vol.4 , pp. 331-338
    • Ray, S.S.1    Bera, R.K.2
  • 145
    • 33644585616 scopus 로고    scopus 로고
    • Numerical solution of semidifferential equations by collocation method
    • E.A. Rawashdeh Numerical solution of semidifferential equations by collocation method Applied Mathematics and Computation 174 2006 869 876
    • (2006) Applied Mathematics and Computation , vol.174 , pp. 869-876
    • Rawashdeh, E.A.1
  • 146
    • 33745698038 scopus 로고    scopus 로고
    • Fractional system identification for lead acid battery state charge estimation
    • J. Sabatier, M. Aoun, A. Oustaloup, G. Gregoire, F. Ragot, and P. Roy Fractional system identification for lead acid battery state charge estimation Signal Processing 86 10 2006 2645 2657
    • (2006) Signal Processing , vol.86 , Issue.10 , pp. 2645-2657
    • Sabatier, J.1    Aoun, M.2    Oustaloup, A.3    Gregoire, G.4    Ragot, F.5    Roy, P.6
  • 149
    • 1642290056 scopus 로고    scopus 로고
    • Comparing numerical methods for the solutions of systems of ordinary differential equations
    • N. Shawagfeh, and D. Kaya Comparing numerical methods for the solutions of systems of ordinary differential equations Applied Mathematics Letters 17 2004 323 328
    • (2004) Applied Mathematics Letters , vol.17 , pp. 323-328
    • Shawagfeh, N.1    Kaya, D.2
  • 150
    • 36849035742 scopus 로고    scopus 로고
    • MR Elastography of breast lesions: Understanding the solid/liquid duality can improve the specificity of contrast-enhanced MR mammography
    • R. Sinkus, K. Siegmann, T. Xydeas, M. Tanter, C. Claussen, and M. Fink MR Elastography of breast lesions: understanding the solid/liquid duality can improve the specificity of contrast-enhanced MR mammography Magnetic Resonance in Medicine 58 2007 1135 1144
    • (2007) Magnetic Resonance in Medicine , vol.58 , pp. 1135-1144
    • Sinkus, R.1    Siegmann, K.2    Xydeas, T.3    Tanter, M.4    Claussen, C.5    Fink, M.6
  • 151
    • 0021424253 scopus 로고
    • Linear approximation for transfer function with a pole of fractional order
    • H. Sun, A. Abdelwahed, and B. Onaral Linear approximation for transfer function with a pole of fractional order IEEE Transactions on Automatic Control 29 5 1984 441 444
    • (1984) IEEE Transactions on Automatic Control , vol.29 , Issue.5 , pp. 441-444
    • Sun, H.1    Abdelwahed, A.2    Onaral, B.3
  • 152
    • 0015989417 scopus 로고
    • Distributed relaxation processes in sensory adaptation
    • J. Thorson, and M. Biederman-Thorson Distributed relaxation processes in sensory adaptation Science 183 1974 161 172
    • (1974) Science , vol.183 , pp. 161-172
    • Thorson, J.1    Biederman-Thorson, M.2
  • 153
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivatives in the behavior of real materials
    • P.J. Torvik, and R.L. Bagley On the appearance of the fractional derivatives in the behavior of real materials Journal of Applied Mechanics (Transaction ASME) 51 2 1984 294 298
    • (1984) Journal of Applied Mechanics (Transaction ASME) , vol.51 , Issue.2 , pp. 294-298
    • Torvik, P.J.1    Bagley, R.L.2
  • 159
    • 33645304553 scopus 로고    scopus 로고
    • Modeling and control of dynamic system using fractional calculus: Application to electrochemical
    • Las Vegas, NV
    • B. Vinagre, V. Feliu, Modeling and control of dynamic system using fractional calculus: application to electrochemical, in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, 2002, pp. 214239.
    • (2002) Proceedings of the 41st IEEE Conference on Decision and Control , pp. 214-239
    • Vinagre, B.1    Feliu, V.2
  • 160
    • 0242270972 scopus 로고    scopus 로고
    • Two direct tustin discretization methods for fractional-order differentiator/integrator
    • B.M. Vinagre, Y.Q. Chen, and I. Petras Two direct tustin discretization methods for fractional-order differentiator/integrator The Journal of Franklin Institute 340 5 2003 349 362
    • (2003) The Journal of Franklin Institute , vol.340 , Issue.5 , pp. 349-362
    • Vinagre, B.M.1    Chen, Y.Q.2    Petras, I.3
  • 161
    • 38149057159 scopus 로고    scopus 로고
    • Optimal fractional controllers for rational order systems: A special case of the WienerHopf spectral factorization method
    • B.M. Vinagre, and V. Feliu Optimal fractional controllers for rational order systems: a special case of the WienerHopf spectral factorization method IEEE Transactions on Automatic Control 52 12 2007 2385 2389
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.12 , pp. 2385-2389
    • Vinagre, B.M.1    Feliu, V.2
  • 163
    • 0016702610 scopus 로고
    • 1/f noise in speech and music
    • R.F. Voss, and J. Clarke 1/f noise in speech and music Nature 258 1975 317 318
    • (1975) Nature , vol.258 , pp. 317-318
    • Voss, R.F.1    Clarke, J.2
  • 164
    • 84972521562 scopus 로고
    • Self-similarity in high-speed packed traffic: Analysis and modelling of ethernet traffic measurements
    • W. Willinger, M.S. Taqqu, W.E. Leland, and V. Wilson Self-similarity in high-speed packed traffic: analysis and modelling of ethernet traffic measurements Statistical Science 10 1 1995 67 85
    • (1995) Statistical Science , vol.10 , Issue.1 , pp. 67-85
    • Willinger, W.1    Taqqu, M.S.2    Leland, W.E.3    Wilson, V.4
  • 170
    • 33748293091 scopus 로고    scopus 로고
    • Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives
    • G.E. Drgnescu Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives Journal of Mathematical Physics 47 8 2006 Art. No. 082902
    • (2006) Journal of Mathematical Physics , vol.47 , Issue.8
    • Drgnescu, G.E.1
  • 173
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration methoda kind of non-linear analytical technique: Some examples
    • J.H. He Variational iteration methoda kind of non-linear analytical technique: some examples International Journal of Nonlinear Mechanics 34 1999 699 708
    • (1999) International Journal of Nonlinear Mechanics , vol.34 , pp. 699-708
    • He, J.H.1
  • 174
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential systems
    • J.H. He Variational iteration method for autonomous ordinary differential systems Applied Mathematics and Computation 114 2000 115 123
    • (2000) Applied Mathematics and Computation , vol.114 , pp. 115-123
    • He, J.H.1
  • 175
    • 0041621600 scopus 로고    scopus 로고
    • Variational principle for some nonlinear partial differential equations with variable coefficients
    • J.H. He Variational principle for some nonlinear partial differential equations with variable coefficients Chaos, Solitons & Fractals 19 4 2004 847 851
    • (2004) Chaos, Solitons & Fractals , vol.19 , Issue.4 , pp. 847-851
    • He, J.H.1
  • 176
    • 0003230865 scopus 로고
    • Analytical and numerical methods for Volterra equations
    • P. Linz Analytical and numerical methods for Volterra equations SIAM Studies in Applied Mathematics 7 1985
    • (1985) SIAM Studies in Applied Mathematics , vol.7
    • Linz, P.1
  • 177
    • 4243080806 scopus 로고    scopus 로고
    • Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method
    • H.M. Liu Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method Chaos, Solitons & Fractals 23 2 2005 573 576
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.2 , pp. 573-576
    • Liu, H.M.1
  • 178
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Z. Odibat, and S. Momani Application of variational iteration method to nonlinear differential equations of fractional order International Journal of Nonlinear Science and Numerical Simulation 1 7 2006 15 27
    • (2006) International Journal of Nonlinear Science and Numerical Simulation , vol.1 , Issue.7 , pp. 15-27
    • Odibat, Z.1    Momani, S.2
  • 179
    • 33749360092 scopus 로고    scopus 로고
    • Fractional statistical mechanics
    • V.E. Tarasov Fractional statistical mechanics Chaos 16 3 2006
    • (2006) Chaos , vol.16 , Issue.3
    • Tarasov, V.E.1


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