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Volumn , Issue 9781447128519, 2012, Pages 1-90

Distributed-order dynamic systems stability, simulation, applications and perspectives

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL ENGINEERING;

EID: 84907285493     PISSN: 21926786     EISSN: 21926794     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (18)

References (130)
  • 1
    • 52349091590 scopus 로고    scopus 로고
    • Identification of complex order-distributions
    • Adams JL, Hartley TT, Lorenzo CF (2008) Identification of complex order-distributions. J Vib Control 14(9-10):1375-1388
    • (2008) J Vib Control , vol.14 , Issue.9-10 , pp. 1375-1388
    • Adams, J.L.1    Hartley, T.T.2    Lorenzo, C.F.3
  • 2
    • 55249087154 scopus 로고    scopus 로고
    • Necessary and sufficient stability condition of fractional-order interval linear systems
    • Ahn HS, Chen YQ (2008) Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica 44(11):2985-2988
    • (2008) Automatica , vol.44 , Issue.11 , pp. 2985-2988
    • Ahn, H.S.1    Chen, Y.Q.2
  • 3
    • 34247502196 scopus 로고    scopus 로고
    • Robust stability test of a class of linear time-invariant interval fractional-order systems using Lyapunov inequality
    • Ahn HS, Chen YQ, Podlubny I (2007) Robust stability test of a class of linear time-invariant interval fractional-order systems using Lyapunov inequality. Appl Math Comput 187(1):27-34
    • (2007) Appl Math Comput , vol.187 , Issue.1 , pp. 27-34
    • Ahn, H.S.1    Chen, Y.Q.2    Podlubny, I.3
  • 6
    • 33845944224 scopus 로고    scopus 로고
    • On a nonlinear distributed order fractional differential equation
    • Atanackovic TM, Oparnica L, Pilipovic S (2007) On a nonlinear distributed order fractional differential equation. J Math Anal Appl 328(1):590-608.
    • (2007) J Math Anal Appl , vol.328 , Issue.1 , pp. 590-608
    • Atanackovic, T.M.1    Oparnica, L.2    Pilipovic, S.3
  • 7
    • 77952873423 scopus 로고    scopus 로고
    • Existence and calculation of the solution to the time distributed order diffusion equation
    • Atanackovic TM, Pilipovic S, Zorica D (2009a) Existence and calculation of the solution to the time distributed order diffusion equation. Phys Scripta T136:014012 (6pp)
    • (2009) Phys Scripta
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 8
    • 67149103784 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. I. Volterra-type equation
    • Atanackovic TM, Pilipovic S, Zorica D (2009b) Time distributed-order diffusion-wave equation. I. Volterra-type equation. Proc Royal Soc A 465:1869-1891.
    • (2009) Proc Royal Soc A , vol.465 , pp. 1869-1891
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 9
    • 67149125441 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
    • Atanackovic TM, Pilipovic S, Zorica D (2009c) Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations. Proc Royal Soc A 465:1893-1917.
    • (2009) Proc Royal Soc A , vol.465 , pp. 1893-1917
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 10
    • 78651225252 scopus 로고    scopus 로고
    • Distributed-order fractional wave equation on a finite domain stress relaxation in a rod
    • Atanackovic TM, Pilipovic S, Zorica D (2011) Distributed-order fractional wave equation on a finite domain stress relaxation in a rod. Int J Eng Sci 49(2):175-190.
    • (2011) Int J Eng Sci , vol.49 , Issue.2 , pp. 175-190
    • Atanackovic, T.M.1    Pilipovic, S.2    Zorica, D.3
  • 11
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Bagley RL, Torvik PJ (1984) On the appearance of the fractional derivative in the behavior of real materials. ASME J Appl Mech 51(2):294-298.
    • (1984) ASME J Appl Mech , vol.51 , Issue.2 , pp. 294-298
    • Bagley, R.L.1    Torvik, P.J.2
  • 12
    • 0001342751 scopus 로고    scopus 로고
    • On the existence of the order domain and the solution of distributed order equations (Parts I, II)
    • Bagley RL, Torvik PJ (2000) On the existence of the order domain and the solution of distributed order equations (Parts I, II). Int J Appl Mech 2(7):865-882, 965-987.
    • (2000) Int J Appl Mech , vol.2 , Issue.7
    • Bagley, R.L.1    Torvik, P.J.2
  • 14
    • 0036642801 scopus 로고    scopus 로고
    • Analysis of fractional delay systems of retarded and neutral type
    • Bonnet C, Partington JR (2002) Analysis of fractional delay systems of retarded and neutral type. Automatica 38(7):1133-1138.
    • (2002) Automatica , vol.38 , Issue.7 , pp. 1133-1138
    • Bonnet, C.1    Partington, J.R.2
  • 15
    • 36348973366 scopus 로고    scopus 로고
    • Stabilization of some fractional delay systems of neutral type
    • Bonnet C, Partington JR (2007) Stabilization of some fractional delay systems of neutral type. Automatica 43(12):2047-2053.
    • (2007) Automatica , vol.43 , Issue.12 , pp. 2047-2053
    • Bonnet, C.1    Partington, J.R.2
  • 18
    • 51249169579 scopus 로고
    • Mean fractional-order-derivatives differential equations and filters
    • Caputo M (1995) Mean fractional-order-derivatives differential equations and filters. Annali dell’Universita di Ferrara 41(1):73-84.
    • (1995) Annali dell’Universita Di Ferrara , vol.41 , Issue.1 , pp. 73-84
    • Caputo, M.1
  • 19
    • 0000227056 scopus 로고    scopus 로고
    • Distributed order differential equations modelling dielectric induction and diffusion
    • Caputo M (2001) Distributed order differential equations modelling dielectric induction and diffusion. Fract Calc Appl Anal 4(4):421-442.
    • (2001) Fract Calc Appl Anal , vol.4 , Issue.4 , pp. 421-442
    • Caputo, M.1
  • 20
    • 84877655853 scopus 로고
    • Approximation of fractional capacitors (1/s)(1/n) by a regular Newton process
    • Carlson G, Halijak C (1964) Approximation of fractional capacitors (1/s)(1/n) by a regular Newton process. IEEE Trans Circuit Theory 11(2):210-213.
    • (1964) IEEE Trans Circuit Theory , vol.11 , Issue.2 , pp. 210-213
    • Carlson, G.1    Halijak, C.2
  • 21
    • 41349088572 scopus 로고    scopus 로고
    • Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations
    • Chechkin AV, Gorenflo R, Sokolov IM (2002) Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations. Phys Rev E 66:046129.
    • (2002) Phys Rev E , vol.66
    • Chechkin, A.V.1    Gorenflo, R.2    Sokolov, I.M.3
  • 22
    • 33745872964 scopus 로고    scopus 로고
    • Robust stability check of fractional order linear time invariant systems with interval uncertainties
    • Chen YQ, Ahn HS, Podlubny I (2006) Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Process 86(10):2611-2618.
    • (2006) Signal Process , vol.86 , Issue.10 , pp. 2611-2618
    • Chen, Y.Q.1    Ahn, H.S.2    Podlubny, I.3
  • 23
    • 76449111034 scopus 로고    scopus 로고
    • Anomalous diffusion modeling by fractal and fractional derivatives
    • Chen W, Sun HG, Zhang XD, Korosak D (2009) Anomalous diffusion modeling by fractal and fractional derivatives. Comput Math Appl 59(5):1754-1758.
    • (2009) Comput Math Appl , vol.59 , Issue.5 , pp. 1754-1758
    • Chen, W.1    Sun, H.G.2    Zhang, X.D.3    Korosak, D.4
  • 25
    • 58549120748 scopus 로고    scopus 로고
    • Numerical analysis for distributed-order differential equations
    • Diethelm K, Ford NJ (2009) Numerical analysis for distributed-order differential equations. J Comput Appl Math 225(1):96-104.
    • (2009) J Comput Appl Math , vol.225 , Issue.1 , pp. 96-104
    • Diethelm, K.1    Ford, N.J.2
  • 26
    • 0141892685 scopus 로고    scopus 로고
    • Fractional-order system identification based on continuous orderdistributions
    • Hartley TT, Lorenzo CF (2003) Fractional-order system identification based on continuous orderdistributions. Signal Process 83(11):2287-2300.
    • (2003) Signal Process , vol.83 , Issue.11 , pp. 2287-2300
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 27
    • 33645135087 scopus 로고    scopus 로고
    • A numerical algorithm for stability testing of fractional delay systems
    • Hwang C, Cheng YC (2006) A numerical algorithm for stability testing of fractional delay systems. Automatica 42(5):825-831.
    • (2006) Automatica , vol.42 , Issue.5 , pp. 825-831
    • Hwang, C.1    Cheng, Y.C.2
  • 28
    • 37449011239 scopus 로고    scopus 로고
    • Distributed order calculus and equations of ultraslow diffusion
    • Kochubei AN (2008) Distributed order calculus and equations of ultraslow diffusion. J Math Anal Appl 340(1):252-281.
    • (2008) J Math Anal Appl , vol.340 , Issue.1 , pp. 252-281
    • Kochubei, A.N.1
  • 29
    • 77649184282 scopus 로고    scopus 로고
    • A fractional order proportional and derivative (Fopd) motion controller: Tuning rule and experiments
    • Li HS, Luo Y, Chen YQ (2009) A fractional order proportional and derivative (fopd) motion controller: tuning rule and experiments. IEEE Trans Control Syst Technol 18(2):1-5.
    • (2009) IEEE Trans Control Syst Technol , vol.18 , Issue.2 , pp. 1-5
    • Li, H.S.1    Luo, Y.2    Chen, Y.Q.3
  • 31
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • Lorenzo CF, Hartley TT (2002) Variable order and distributed order fractional operators. Nonlinear Dyn 29(1-4):57-98.
    • (2002) Nonlinear Dyn , vol.29 , Issue.1-4 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 32
    • 67649619829 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional-order interval systems: An lmi approach
    • Lu JG, Chen GR (2009) Robust stability and stabilization of fractional-order interval systems: an lmi approach. IEEE Trans Autom Control 54(6):1294-1299.
    • (2009) IEEE Trans Autom Control , vol.54 , Issue.6 , pp. 1294-1299
    • Lu, J.G.1    Chen, G.R.2
  • 33
    • 75449099727 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional order interval systems with the fractional order Α: The 0 < Α < 1. case
    • Lu JG, Chen YQ (2010) Robust stability and stabilization of fractional order interval systems with the fractional order Α: The 0 < Α < 1. case. IEEE Trans Autom Control 55(1):152-158.
    • (2010) IEEE Trans Autom Control , vol.55 , Issue.1 , pp. 152-158
    • Lu, J.G.1    Chen, Y.Q.2
  • 35
    • 34547102267 scopus 로고    scopus 로고
    • The role of the fox-wright functions in fractional sub-diffusion of distributed order
    • Mainardi F, Pagnini G (2007) The role of the fox-wright functions in fractional sub-diffusion of distributed order. J Comput Appl Math 207(2):245-257.
    • (2007) J Comput Appl Math , vol.207 , Issue.2 , pp. 245-257
    • Mainardi, F.1    Pagnini, G.2
  • 36
    • 34748907169 scopus 로고    scopus 로고
    • The two forms of fractional relaxation of distributed order
    • Mainardi F, Mura A, Gorenflo R, Stojanovic M (2007a) The two forms of fractional relaxation of distributed order. J Vib Control 9:1249-1268.
    • (2007) J Vib Control , vol.9 , pp. 1249-1268
    • Mainardi, F.1    Mura, A.2    Gorenflo, R.3    Stojanovic, M.4
  • 37
    • 34247367101 scopus 로고    scopus 로고
    • Some aspects of fractional diffusion equations of single and distributed order
    • Mainardi F, Mura A, Pagnini G, Gorenflo R (2007b) Some aspects of fractional diffusion equations of single and distributed order. Appl Math Comput 187:295-305.
    • (2007) Appl Math Comput , vol.187 , pp. 295-305
    • Mainardi, F.1    Mura, A.2    Pagnini, G.3    Gorenflo, R.4
  • 38
    • 52349083860 scopus 로고    scopus 로고
    • Time-fractional diffusion of distributed order
    • Mainardi F, Mura A, Pagnini G, Gorenflo R (2008) Time-fractional diffusion of distributed order. J Vib Control 14(9-10):1267-1290.
    • (2008) J Vib Control , vol.14 , Issue.9-10 , pp. 1267-1290
    • Mainardi, F.1    Mura, A.2    Pagnini, G.3    Gorenflo, R.4
  • 40
    • 79952184887 scopus 로고    scopus 로고
    • Distributed-order fractional diffusions on bounded domains
    • Meerschaert MM, Nane E, Vellaisamy P (2011) Distributed-order fractional diffusions on bounded domains. J Math Anal Appl 379:216-228.
    • (2011) J Math Anal Appl , vol.379 , pp. 216-228
    • Meerschaert, M.M.1    Nane, E.2    Vellaisamy, P.3
  • 42
    • 85019485305 scopus 로고
    • The crone control of resonant plants: Application to a flexible transmission
    • Oustaloup A, Mathieu B, Lanusse P (1995) The crone control of resonant plants: application to a flexible transmission. Eur J Control 1(2):113-121.
    • (1995) Eur J Control , vol.1 , Issue.2 , pp. 113-121
    • Oustaloup, A.1    Mathieu, B.2    Lanusse, P.3
  • 44
    • 0032653954 scopus 로고    scopus 로고
    • Fractional-order systems and PIΛDΜ controllers
    • Podlubny I (1999) Fractional-order systems and PIΛDΜ controllers. IEEE Trans Autom Control 44(1):208-214.
    • (1999) IEEE Trans Autom Control , vol.44 , Issue.1 , pp. 208-214
    • Podlubny, I.1
  • 46
    • 53449102089 scopus 로고    scopus 로고
    • Lévy flights in nonhomogeneous media: Distributed-order fractional equation approach
    • Srokowski T (2008) Lévy flights in nonhomogeneous media: distributed-order fractional equation approach. Phys Rev E 78(3):031135.
    • (2008) Phys Rev E , vol.78 , Issue.3
    • Srokowski, T.1
  • 47
    • 68649098514 scopus 로고    scopus 로고
    • Variable-order fractional differential operators in anomalous diffusion modeling
    • Sun HG, Chen W, Chen YQ (2009) Variable-order fractional differential operators in anomalous diffusion modeling. Phys A: Stat Mech Appl 388(21):4586-4592.
    • (2009) Phys A: Stat Mech Appl , vol.388 , Issue.21 , pp. 4586-4592
    • Sun, H.G.1    Chen, W.2    Chen, Y.Q.3
  • 48
    • 73749087815 scopus 로고    scopus 로고
    • On mean square displacement behaviors of anomalous diffusions with variable and random orders
    • Sun HG, Chen W, Sheng H, Chen YQ (2010) On mean square displacement behaviors of anomalous diffusions with variable and random orders. Phys Lett A 374(7):906-910.
    • (2010) Phys Lett A , vol.374 , Issue.7 , pp. 906-910
    • Sun, H.G.1    Chen, W.2    Sheng, H.3    Chen, Y.Q.4
  • 50
    • 77957363180 scopus 로고    scopus 로고
    • Random walk models associated with distributed fractional order differential equations
    • Umarov S, Steinberg S (2006) Random walk models associated with distributed fractional order differential equations. Inst Math Stat 51:117-127.
    • (2006) Inst Math Stat , vol.51 , pp. 117-127
    • Umarov, S.1    Steinberg, S.2
  • 51
    • 33745759950 scopus 로고    scopus 로고
    • Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics
    • Xu MY, Tan WC (2006) Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics. Sci China: Ser G Phys Mech Astron 49(3):257-272
    • (2006) Sci China: Ser G Phys Mech Astron , vol.49 , Issue.3 , pp. 257-272
    • Xu, M.Y.1    Tan, W.C.2
  • 56
    • 0141892685 scopus 로고    scopus 로고
    • Fractional-order system identification based on continuous orderdistributions
    • Hartley TT, Lorenzo CF (2003) Fractional-order system identification based on continuous orderdistributions. Signal Process 83(11):2287–2300
    • (2003) Signal Process , vol.83 , Issue.11 , pp. 2287-2300
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 57
    • 15544366107 scopus 로고    scopus 로고
    • A frequency-domain approach to optimal fractional-order damping
    • Hartley TT, Lorenzo CF (2004) A frequency-domain approach to optimal fractional-order damping. Nonlinear Dyn 38(1–2):69–84
    • (2004) Nonlinear Dyn , vol.38 , Issue.1-2 , pp. 69-84
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 58
    • 79551493680 scopus 로고    scopus 로고
    • On distributed order integrator/differentiator
    • Li Y, Sheng H, Chen YQ (2010) On distributed order integrator/differentiator. Signal Process 91(5):1079–1084
    • (2010) Signal Process , vol.91 , Issue.5 , pp. 1079-1084
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 62
    • 55249087154 scopus 로고    scopus 로고
    • Necessary and sufficient stability condition of fractional-order interval linear systems
    • Ahn HS, Chen YQ (2008) Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica 44(11):2985-2988
    • (2008) Automatica , vol.44 , Issue.11 , pp. 2985-2988
    • Ahn, H.S.1    Chen, Y.Q.2
  • 63
    • 34247502196 scopus 로고    scopus 로고
    • Robust stability test of a class of linear time-invariant interval fractional-order systems using Lyapunov inequality
    • Ahn HS, Chen YQ, Podlubny I (2007) Robust stability test of a class of linear time-invariant interval fractional-order systems using Lyapunov inequality. Appl Math Comput 187(1):27-34
    • (2007) Appl Math Comput , vol.187 , Issue.1 , pp. 27-34
    • Ahn, H.S.1    Chen, Y.Q.2    Podlubny, I.3
  • 64
    • 0036642801 scopus 로고    scopus 로고
    • Analysis of fractional delay systems of retarded and neutral type
    • Bonnet C, Partington JR (2002) Analysis of fractional delay systems of retarded and neutral type. Automatica 38(7):1133-1138
    • (2002) Automatica , vol.38 , Issue.7 , pp. 1133-1138
    • Bonnet, C.1    Partington, J.R.2
  • 65
    • 36348973366 scopus 로고    scopus 로고
    • Stabilization of some fractional delay systems of neutral type
    • Bonnet C, Partington JR (2007) Stabilization of some fractional delay systems of neutral type. Automatica 43(12):2047-2053
    • (2007) Automatica , vol.43 , Issue.12 , pp. 2047-2053
    • Bonnet, C.1    Partington, J.R.2
  • 66
    • 33745872964 scopus 로고    scopus 로고
    • Robust stability check of fractional order linear time invariant systems with interval uncertainties
    • Chen YQ, Ahn HS, Podlubny I (2006) Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Process 86(10):2611-2618
    • (2006) Signal Process , vol.86 , Issue.10 , pp. 2611-2618
    • Chen, Y.Q.1    Ahn, H.S.2    Podlubny, I.3
  • 67
    • 33645135087 scopus 로고    scopus 로고
    • A numerical algorithm for stability testing of fractional delay systems
    • Hwang C, Cheng YC (2006) A numerical algorithm for stability testing of fractional delay systems. Automatica 42(5):825-831
    • (2006) Automatica , vol.42 , Issue.5 , pp. 825-831
    • Hwang, C.1    Cheng, Y.C.2
  • 68
    • 78049326583 scopus 로고    scopus 로고
    • Analytical impulse response of a fractional second order filter and its impulse response invariant discretization
    • Li Y, Sheng H, Chen YQ (2011) Analytical impulse response of a fractional second order filter and its impulse response invariant discretization. Signal Process 91(3):498-507
    • (2011) Signal Process , vol.91 , Issue.3 , pp. 498-507
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 69
    • 75449099727 scopus 로고    scopus 로고
    • Robust stability and stabilization of fractional order interval systems with the fractional order Α: The 0 < Α < 1 case
    • Lu JG, Chen YQ (2010) Robust stability and stabilization of fractional order interval systems with the fractional order Α: the 0 < Α < 1 case. IEEE Trans Autom Control 55(1):152-158
    • (2010) IEEE Trans Autom Control , vol.55 , Issue.1 , pp. 152-158
    • Lu, J.G.1    Chen, Y.Q.2
  • 74
    • 52349091590 scopus 로고    scopus 로고
    • Identification of complex order-distributions
    • Adams JL, Hartley TT, Lorenzo CF (2008) Identification of complex order-distributions. J Vib Control 14(9-10):1375-1388
    • (2008) J Vib Control , vol.14 , Issue.9-10 , pp. 1375-1388
    • Adams, J.L.1    Hartley, T.T.2    Lorenzo, C.F.3
  • 75
    • 44649104914 scopus 로고    scopus 로고
    • Implementation of discrete-time fractional-order controllers based on LS approximations
    • Barbosa RS, Machado JAT (2006) Implementation of discrete-time fractional-order controllers based on LS approximations. Acta Polytech Hung 3(4):5-22
    • (2006) Acta Polytech Hung , vol.3 , Issue.4 , pp. 5-22
    • Barbosa, R.S.1    Machado, J.2
  • 80
    • 0036506044 scopus 로고    scopus 로고
    • Discretization schemes for fractional-order differentiators and integrators
    • Chen YQ, Moore KL (2002) Discretization schemes for fractional-order differentiators and integrators. IEEE Trans Circuits Syst I Fundam Theory Appl 49(3):363-367
    • (2002) IEEE Trans Circuits Syst I Fundam Theory Appl , vol.49 , Issue.3 , pp. 363-367
    • Chen, Y.Q.1    Moore, K.L.2
  • 81
    • 0141961689 scopus 로고    scopus 로고
    • A new IIR-type digital fractional order differentiator
    • Chen YQ, Vinagre BM (2003) A new IIR-type digital fractional order differentiator. Signal Process 83(11):2359-2365
    • (2003) Signal Process , vol.83 , Issue.11 , pp. 2359-2365
    • Chen, Y.Q.1    Vinagre, B.M.2
  • 82
    • 15544372160 scopus 로고    scopus 로고
    • Continued fraction expansion approaches to discretizing fractional order derivatives—an expository review
    • Dec
    • Chen YQ, Vinagre BM, Podlubny I (2004) Continued fraction expansion approaches to discretizing fractional order derivatives—an expository review. Nonlinear Dyn 38(16):155-170, Dec 2004
    • (2004) Nonlinear Dyn , vol.38 , Issue.16 , pp. 155-170
    • Chen, Y.Q.1    Vinagre, B.M.2    Podlubny, I.3
  • 83
    • 77953332285 scopus 로고    scopus 로고
    • Applications of fractional calculus
    • Dalir M, Bashour M (2010) Applications of fractional calculus. Appl Math Sci 4(21-24):1021-1032
    • (2010) Appl Math Sci , vol.4 , Issue.21-24 , pp. 1021-1032
    • Dalir, M.1    Bashour, M.2
  • 85
    • 52349116154 scopus 로고    scopus 로고
    • Design of optimum systems of viscoelastic vibration absorbers for a given material based on the fractional calculus model
    • De Espíndola JJ, Bavastri CA, De Oliveira Lopes EM (2008) Design of optimum systems of viscoelastic vibration absorbers for a given material based on the fractional calculus model. J Vib Control 14(9-10):1607-1630
    • (2008) J Vib Control , vol.14 , Issue.9-10 , pp. 1607-1630
    • De Espíndola, J.J.1    Bavastri, C.A.2    De Oliveira Lopes, E.M.3
  • 87
    • 68049113238 scopus 로고    scopus 로고
    • Impulse invariance-based method for the computation of fractional integral of order 0 < Α < 1
    • Ferdi Y (2009) Impulse invariance-based method for the computation of fractional integral of order 0 < Α < 1. Comput Electr Eng 35(5):722-729
    • (2009) Comput Electr Eng , vol.35 , Issue.5 , pp. 722-729
    • Ferdi, Y.1
  • 88
    • 0141892685 scopus 로고    scopus 로고
    • Fractional-order system identification based on continuous orderdistributions
    • Hartley TT, Lorenzo CF (2003) Fractional-order system identification based on continuous orderdistributions. Signal Process 83(11):2287-2300
    • (2003) Signal Process , vol.83 , Issue.11 , pp. 2287-2300
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 89
    • 15544366107 scopus 로고    scopus 로고
    • A frequency-domain approach to optimal fractional-order damping
    • Hartley TT, Lorenzo CF (2004) A frequency-domain approach to optimal fractional-order damping. Nonlinear Dyn 38(1-2):69-84
    • (2004) Nonlinear Dyn , vol.38 , Issue.1-2 , pp. 69-84
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 90
    • 0021440218 scopus 로고
    • Applications of fractional calculus to the theory of viscoelasticity
    • Koeller RC (1984) Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech 51(2):299-307
    • (1984) J Appl Mech , vol.51 , Issue.2 , pp. 299-307
    • Koeller, R.C.1
  • 93
    • 79551493680 scopus 로고    scopus 로고
    • On distributed order integrator/differentiator
    • Li Y, Sheng H, Chen YQ (2010b) On distributed order integrator/differentiator. Signal Process 91(5):1079-1084
    • (2010) Signal Process , vol.91 , Issue.5 , pp. 1079-1084
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 94
    • 78049326583 scopus 로고    scopus 로고
    • Analytical impulse response of a fractional second order filter and its impulse response invariant discretization
    • Li Y, Sheng H, Chen YQ (2011) Analytical impulse response of a fractional second order filter and its impulse response invariant discretization. Signal Process 91(3):498-507
    • (2011) Signal Process , vol.91 , Issue.3 , pp. 498-507
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 95
    • 0031285474 scopus 로고    scopus 로고
    • On the thermodynamics of fractional damping elements
    • Lion A (1997) On the thermodynamics of fractional damping elements. Continuum Mech Thermodyn 9(2):83-96
    • (1997) Continuum Mech Thermodyn , vol.9 , Issue.2 , pp. 83-96
    • Lion, A.1
  • 96
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • Lorenzo CF, Hartley TT (2002) Variable order and distributed order fractional operators. Nonlinear Dyn 29(1-4):57-98
    • (2002) Nonlinear Dyn , vol.29 , Issue.1-4 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 97
    • 0000717432 scopus 로고
    • Discretized fractional calculus
    • Lubich C (1986) Discretized fractional calculus. SIAM J Math Anal 17(3):704-719
    • (1986) SIAM J Math Anal , vol.17 , Issue.3 , pp. 704-719
    • Lubich, C.1
  • 98
    • 0030651602 scopus 로고    scopus 로고
    • Analysis and design of fractional-order digital control systems
    • Machado JAT (1997) Analysis and design of fractional-order digital control systems. Syst Anal Model Simul 27(2-3):107-122
    • (1997) Syst Anal Model Simul , vol.27 , Issue.2-3 , pp. 107-122
    • Machado, J.1
  • 100
    • 0019623026 scopus 로고
    • Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation
    • Oustaloup A (1981) Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation. IEEE Trans Circuits Syst 28(10):1007-1009
    • (1981) IEEE Trans Circuits Syst , vol.28 , Issue.10 , pp. 1007-1009
    • Oustaloup, A.1
  • 102
    • 0023859640 scopus 로고
    • General response of viscoelastic systems modelled by fractional operators
    • Padovan J, Guo YH (1988) General response of viscoelastic systems modelled by fractional operators. J Frankl Inst 325(2):247-275
    • (1988) J Frankl Inst , vol.325 , Issue.2 , pp. 247-275
    • Padovan, J.1    Guo, Y.H.2
  • 105
    • 50549083034 scopus 로고    scopus 로고
    • Fractional-order sinusoidal oscillators: Design procedure and practical examples
    • Radwan AG, Elwakil AS, Soliman AM (2008) Fractional-order sinusoidal oscillators: design procedure and practical examples. IEEE Trans Circuits Syst I Regul Pap 55(7):2051-2063
    • (2008) IEEE Trans Circuits Syst I Regul Pap , vol.55 , Issue.7 , pp. 2051-2063
    • Radwan, A.G.1    Elwakil, A.S.2    Soliman, A.M.3
  • 106
    • 0030736195 scopus 로고    scopus 로고
    • Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems
    • Rossikhin YA, Shitikova MV (1997) Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems. Acta Mech 120(1-4):109-125
    • (1997) Acta Mech , vol.120 , Issue.1-4 , pp. 109-125
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 107
    • 33750605555 scopus 로고    scopus 로고
    • Tunedmass damperwith fractional derivative damping
    • Rüdinger F (2006) Tunedmass damperwith fractional derivative damping. Eng Struct 28(13):1774-1779
    • (2006) Eng Struct , vol.28 , Issue.13 , pp. 1774-1779
    • Rüdinger, F.1
  • 109
    • 47249146565 scopus 로고    scopus 로고
    • Fractional order filter enhanced LQR for seismic protection of civil structures
    • Shafieezadeh A, Ryan K, Chen YQ (2008) Fractional order filter enhanced LQR for seismic protection of civil structures. J Comput Nonlinear Dyn 3(2):020201.1-021404.7
    • (2008) J Comput Nonlinear Dyn , vol.3 , Issue.2
    • Shafieezadeh, A.1    Ryan, K.2    Chen, Y.Q.3
  • 110
    • 0033471671 scopus 로고    scopus 로고
    • A comparison of numerical methods applied to a fractional model of damping materials
    • Shokooh A (1999) A comparison of numerical methods applied to a fractional model of damping materials. J Vib Control 5(3):331-354
    • (1999) J Vib Control , vol.5 , Issue.3 , pp. 331-354
    • Shokooh, A.1
  • 111
    • 84892149890 scopus 로고
    • A technique for the identification of linear systems
    • Steiglitz K, McBride L (1965) A technique for the identification of linear systems. IEEE Trans Autom Control 10(4):461-464
    • (1965) IEEE Trans Autom Control , vol.10 , Issue.4 , pp. 461-464
    • Steiglitz, K.1    McBride, L.2
  • 112
    • 75149129941 scopus 로고    scopus 로고
    • Notes on integral performance indices in fractional-order control systems
    • Tavazoei MS (2010) Notes on integral performance indices in fractional-order control systems. J Process Control 20(3):285-291
    • (2010) J Process Control , vol.20 , Issue.3 , pp. 285-291
    • Tavazoei, M.S.1
  • 113
    • 0242270972 scopus 로고    scopus 로고
    • Two direct Tustin discretization methods for fractional-order differentiator/integrator
    • Vinagre BM, Chen YQ, Petras I (2003) Two direct Tustin discretization methods for fractional-order differentiator/integrator. J Frankl Inst 340(5):349-362
    • (2003) J Frankl Inst , vol.340 , Issue.5 , pp. 349-362
    • Vinagre, B.M.1    Chen, Y.Q.2    Petras, I.3
  • 116
    • 0034320029 scopus 로고    scopus 로고
    • The ubiquitous Kronecker product
    • Loan CFV (2000) The ubiquitous Kronecker product. J Comput Appl Math 123:85-100
    • (2000) J Comput Appl Math , vol.123 , pp. 85-100
    • Loan, C.1
  • 117
    • 33749526684 scopus 로고    scopus 로고
    • Riesz potential operators and inverses via fractional centred derivatives
    • Ortigueira MD (2006) Riesz potential operators and inverses via fractional centred derivatives. Int J Math Math Sci 48391:1-12
    • (2006) Int J Math Math Sci , vol.48391 , pp. 1-12
    • Ortigueira, M.D.1
  • 118
    • 38749093369 scopus 로고    scopus 로고
    • On the relation between the fractional Brownian motion and the fractional derivatives
    • Ortigueira MD, Batista AG (2008) On the relation between the fractional Brownian motion and the fractional derivatives. Phys Lett A 372:958-968
    • (2008) Phys Lett A , vol.372 , pp. 958-968
    • Ortigueira, M.D.1    Batista, A.G.2
  • 119
    • 33744801528 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus
    • Podlubny I (2000) Matrix approach to discrete fractional calculus. Fract Cal Appl Anal 3(4):359-386
    • (2000) Fract Cal Appl Anal , vol.3 , Issue.4 , pp. 359-386
    • Podlubny, I.1
  • 123
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus ii: Partial fractional differential equations
    • Podlubny I, Chechkin A, Skovranek T, Chen YQ, Vinarge BM (2009b) Matrix approach to discrete fractional calculus ii: partial fractional differential equations. J Comput Phys 228(8):3137-3153
    • (2009) J Comput Phys , vol.228 , Issue.8 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.2    Skovranek, T.3    Chen, Y.Q.4    Vinarge, B.M.5
  • 124
    • 84863605309 scopus 로고    scopus 로고
    • Proceedings of the ASME 2011 international design engineering technical conferences and computers and information in engineering conference IDETC/CIE 2011 August 28-31, 2011, Washington, DC, USA, article DETC2011-47623
    • Podlubny I, Skovranek T, Verbickij V, Vinagre BM, Chen YQ, Petras I (2011) Discrete fractional calculus: non-equidistant grids and variable step length. In: Proceedings of the ASME 2011 international design engineering technical conferences and computers and information in engineering conference IDETC/CIE 2011 August 28-31, 2011, Washington, DC, USA, article DETC2011-47623
    • (2011) Discrete Fractional Calculus: Non-Equidistant Grids and Variable Step Length
    • Podlubny, I.1    Skovranek, T.2    Verbickij, V.3    Vinagre, B.M.4    Chen, Y.Q.5    Petras, I.6
  • 128
    • 77649184282 scopus 로고    scopus 로고
    • A fractional order proportional and derivative (FOPD) motion controller: Tuning rule and experiments
    • Li HS, Luo Y, Chen YQ (2009) A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments. IEEE Trans Control Syst Technol 18(2):1-5
    • (2009) IEEE Trans Control Syst Technol , vol.18 , Issue.2 , pp. 1-5
    • Li, H.S.1    Luo, Y.2    Chen, Y.Q.3
  • 129
    • 70049104872 scopus 로고    scopus 로고
    • Fractional order [proportional derivative] controller for a class of fractional order systems
    • Luo Y, Chen YQ (2009) Fractional order [proportional derivative] controller for a class of fractional order systems. Automatica 45(10):2446-2450
    • (2009) Automatica , vol.45 , Issue.10 , pp. 2446-2450
    • Luo, Y.1    Chen, Y.Q.2


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