메뉴 건너뛰기




Volumn 236, Issue 16, 2012, Pages 4027-4041

Analytical and numerical methods for the stability analysis of linear fractional delay differential equations

Author keywords

Argument Principle; Asymptotic stability; BIBO stability; Fractional differential equation; Laplace transform; Method of steps

Indexed keywords

ANALYTICAL AND NUMERICAL METHODS; ARGUMENT PRINCIPLE; BIBO STABILITY; CHARACTERISTIC EQUATION; COMPARISON RESULT; DELAY DIFFERENTIAL EQUATIONS; FRACTIONAL DELAY; FRACTIONAL DIFFERENTIAL EQUATIONS; LAPLACE TRANSFORM METHOD; METHOD OF STEPS; MITTAG-LEFFLER FUNCTIONS; NUMERICAL APPROACHES; STABILITY ANALYSIS; STABILITY REGIONS;

EID: 84861729690     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2012.03.010     Document Type: Article
Times cited : (90)

References (34)
  • 1
    • 27744581031 scopus 로고    scopus 로고
    • Application of fractional calculus to the modeling of dielectric relaxation phenomena in polymeric materials
    • DOI 10.1002/app.22057
    • E. Reyes-Melo, J. Martinez-Vega, C. Guerrero-Salazar, and U. Ortiz-Mendez Application of fractional calculus to the modeling of dielectric relaxation phenomena in polymeric materials Journal of Applied Polymer Science 98 2005 923 935 (Pubitemid 41583876)
    • (2005) Journal of Applied Polymer Science , vol.98 , Issue.2 , pp. 923-935
    • Reyes-Melo, E.1    Martinez-Vega, J.2    Guerrero-Salazar, C.3    Ortiz-Mendez, U.4
  • 2
    • 0001488637 scopus 로고
    • Fractal rheological models and fractional differential equations for viscoelastic behavior
    • N. Heymans, and J.-C. Bauwens Fractal rheological models and fractional differential equations for viscoelastic behavior Rheologica Acta 33 1994 210 219
    • (1994) Rheologica Acta , vol.33 , pp. 210-219
    • Heymans, N.1    Bauwens, J.-C.2
  • 4
    • 0036306866 scopus 로고    scopus 로고
    • Existence of turing instabilities in a two-species fractional reaction-diffusion system
    • DOI 10.1137/S0036139900375227, PII S0036139900375227
    • B. Henry, and S. Wearne Existence of Turing instabilities in a two-species fractional reaction-diffusion system SIAM Journal on Applied Mathematics 62 2002 870 887 (Pubitemid 34750573)
    • (2002) SIAM Journal on Applied Mathematics , vol.62 , Issue.3 , pp. 870-887
    • Henry, B.I.1    Wearne, S.L.2
  • 5
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Physics Reports 339 2000 1 77
    • (2000) Physics Reports , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 6
    • 45849155458 scopus 로고    scopus 로고
    • Fractional langevin model of memory in financial markets
    • S. Picozzi, and B.J. West Fractional langevin model of memory in financial markets Physical Review E 66 2002 46 118
    • (2002) Physical Review e , vol.66 , pp. 46-118
    • Picozzi, S.1    West, B.J.2
  • 7
    • 0028878140 scopus 로고
    • A fractional calculus approach to self-similar protein dynamics
    • W. Glockle, and T. Nonnenmacher A fractional calculus approach to self-similar protein dynamics Biophysical Journal 68 1995 46 53
    • (1995) Biophysical Journal , vol.68 , pp. 46-53
    • Glockle, W.1    Nonnenmacher, T.2
  • 9
    • 80052954741 scopus 로고    scopus 로고
    • Chaos in a fractional-order dynamical model of love and its control
    • S. Li, X. Wang, Y. Okazaki, J. Kawabe, T. Murofushi, L. Guan, Advances in Intelligent and Soft Computing Springer Berlin, Heidelberg
    • R. Gu, and Y. Xu Chaos in a fractional-order dynamical model of love and its control S. Li, X. Wang, Y. Okazaki, J. Kawabe, T. Murofushi, L. Guan, Nonlinear Mathematics for Uncertainty and its Applications Advances in Intelligent and Soft Computing vol. 100 2011 Springer Berlin, Heidelberg 349 356
    • (2011) Nonlinear Mathematics for Uncertainty and Its Applications , vol.100 , pp. 349-356
    • Gu, R.1    Xu, Y.2
  • 13
    • 84655169609 scopus 로고    scopus 로고
    • Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions
    • E. Kaslik, and S. Sivasundaram Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions Nonlinear Analysis. Real World Applications 13 2012 1489 1497
    • (2012) Nonlinear Analysis. Real World Applications , vol.13 , pp. 1489-1497
    • Kaslik, E.1    Sivasundaram, S.2
  • 16
    • 79953701362 scopus 로고    scopus 로고
    • A survey on the stability of fractional differential equations
    • C. Li, and F. Zhang A survey on the stability of fractional differential equations The European Physical Journal Special Topics 193 2011 27 47
    • (2011) The European Physical Journal Special Topics , vol.193 , pp. 27-47
    • Li, C.1    Zhang, F.2
  • 18
    • 38949212976 scopus 로고    scopus 로고
    • Some results of linear fractional order time-delay system
    • DOI 10.1016/j.amc.2007.07.069, PII S0096300307007898
    • X. Zhang Some results of linear fractional order time-delay system Applied Mathematics and Computation 197 2008 407 411 (Pubitemid 351215508)
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.1 , pp. 407-411
    • Zhang, X.1
  • 19
    • 0035648796 scopus 로고    scopus 로고
    • Stabilization of fractional exponential systems including delays
    • C. Bonnet, and J.R. Partington Stabilization of fractional exponential systems including delays Kybernetika 37 2001 345 353 (Pubitemid 33391229)
    • (2001) Kybernetika , vol.37 , Issue.3 , pp. 345-353
    • Bonnet, C.1    Partington, J.R.2
  • 20
    • 33645135087 scopus 로고    scopus 로고
    • A numerical algorithm for stability testing of fractional delay systems
    • C. Hwang, and Y.-C. Cheng A numerical algorithm for stability testing of fractional delay systems Automatica 42 2006 825 831
    • (2006) Automatica , vol.42 , pp. 825-831
    • Hwang, C.1    Cheng, Y.-C.2
  • 21
    • 57749209882 scopus 로고    scopus 로고
    • Stability of linear continuous-time fractional order systems with delays of the retarded type
    • M. Busowicz Stability of linear continuous-time fractional order systems with delays of the retarded type Bulletin of the Polish Academy of Sciences 56 2008 319 324
    • (2008) Bulletin of the Polish Academy of Sciences , vol.56 , pp. 319-324
    • Busowicz, M.1
  • 22
    • 0036650867 scopus 로고    scopus 로고
    • Analytical stability bound for a class of delayed fractional-order dynamic systems
    • DOI 10.1023/A:1016591006562, Fractional Order Calculus and Its Applications
    • Y. Chen, and K.L. Moore Analytical stability bound for a class of delayed fractional-order dynamic systems Nonlinear Dynamics 29 2002 191 200 (Pubitemid 34945398)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 191-200
    • Chen, Y.1    Moore, K.L.2
  • 23
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • DOI 10.1007/s11071-006-9094-0
    • W. Deng, C. Li, and J. Lu Stability analysis of linear fractional differential system with multiple time delays Nonlinear Dynamics 48 2007 409 416 (Pubitemid 46407957)
    • (2007) Nonlinear Dynamics , vol.48 , Issue.4 , pp. 409-416
    • Deng, W.1    Li, C.2    Lu, J.3
  • 25
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus, integral and differential equations of fractional order
    • A. Carpinteri, F. Mainardi, CISM Courses and Lecture Notes Springer Verlag Wien
    • R. Gorenflo, and F. Mainardi Fractional calculus, integral and differential equations of fractional order A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics CISM Courses and Lecture Notes vol. 378 1997 Springer Verlag Wien 223 276
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , vol.378 , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 26
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-Leffler stability of fractional order nonlinear dynamic systems
    • Y. Li, Y. Chen, and I. Podlubny Mittag-Leffler stability of fractional order nonlinear dynamic systems Automatica 45 2009 1965 1969
    • (2009) Automatica , vol.45 , pp. 1965-1969
    • Li, Y.1    Chen, Y.2    Podlubny, I.3
  • 27
    • 34249883566 scopus 로고    scopus 로고
    • Lecture notes: The final value theorem revisited - Infinite limits and irrational functions
    • DOI 10.1109/MCS.2007.365008
    • J. Chen, K.H. Lundberg, D.E. Davison, and D.S. Bernstein The final value theorem revisited: infinite limits and irrational functions IEEE Control Systems Magazine 27 2007 97 99 (Pubitemid 46864831)
    • (2007) IEEE Control Systems Magazine , vol.27 , Issue.3 , pp. 97-99
    • Chen, J.1    Lundberg, K.H.2    Davison, D.E.3    Bernstein, D.S.4
  • 28
    • 0036650827 scopus 로고    scopus 로고
    • Dynamics and control of initialized fractional-order systems
    • DOI 10.1023/A:1016534921583, Fractional Order Calculus and Its Applications
    • T. Hartley, and C. Lorenzo Dynamics and control of initialized fractional-order systems Nonlinear Dynamics 29 2002 201 233 (Pubitemid 34945399)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 201-233
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 29
    • 47249104351 scopus 로고    scopus 로고
    • Initialization of fractional-order operators and fractional differential equations
    • C. Lorenzo, and T. Hartley Initialization of fractional-order operators and fractional differential equations Journal of Computational and Nonlinear Dynamics 3 2008 021101:1 021101:9
    • (2008) Journal of Computational and Nonlinear Dynamics , vol.3 , pp. 0211011-0211019
    • Lorenzo, C.1    Hartley, T.2
  • 31
    • 84859707502 scopus 로고    scopus 로고
    • Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform
    • T. Kalmár-Nagy Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform Differential Equations and Dynamical Systems 17 2009 185 200
    • (2009) Differential Equations and Dynamical Systems , vol.17 , pp. 185-200
    • Kalmár-Nagy, T.1
  • 33
    • 55349106156 scopus 로고    scopus 로고
    • Numerical algorithm for calculating the generalized Mittag-Leffler function
    • H. Seybold, and R. Hilfer Numerical algorithm for calculating the generalized Mittag-Leffler function SIAM Journal on Numerical Analysis 47 2008 69 88
    • (2008) SIAM Journal on Numerical Analysis , vol.47 , pp. 69-88
    • Seybold, H.1    Hilfer, R.2
  • 34
    • 0010692330 scopus 로고
    • Method of harmonic analysis in control theory
    • A. Mikhailov Method of harmonic analysis in control theory Automatika i Telemehanika 3 1938 27 81
    • (1938) Automatika i Telemehanika , vol.3 , pp. 27-81
    • Mikhailov, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.