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Volumn 2011, Issue , 2011, Pages

Asymptotical stability of nonlinear fractional differential system with Caputo derivative

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EID: 84860329588     PISSN: 16879643     EISSN: 16879651     Source Type: Journal    
DOI: 10.1155/2011/635165     Document Type: Article
Times cited : (63)

References (24)
  • 1
    • 0021440218 scopus 로고
    • Applications of fractional calculus to the theory of viscoelasticity
    • R. C. Koeller, "Applications of fractional calculus to the theory of viscoelasticity," Journal of Applied Mechanics, Vol. 51, no. 2, pp. 299-307, 1984. (Pubitemid 14583151)
    • (1984) Journal of Applied Mechanics, Transactions ASME , vol.51 , Issue.2 , pp. 299-307
    • Koeller, R.C.1
  • 3
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • D. Matignon, "Stability results for fractional differential equations with applications to control processing," in Proceedings of the IMACS-SMC, Vol. 2, pp. 963-968, 1996.
    • (1996) Proceedings of the IMACS-SMC , vol.2 , pp. 963-968
    • Matignon, D.1
  • 4
    • 34250899368 scopus 로고    scopus 로고
    • Analysis of fractional differential equations with multi-orders
    • DOI 10.1142/S0218348X07003472, PII S0218348X07003472
    • W. H. Deng, C. P. Li, and Q. Guo, "Analysis of fractional differential equations with multi-orders," Fractals, Vol. 15, no. 2, pp. 173-182, 2007. (Pubitemid 46970248)
    • (2007) Fractals , vol.15 , Issue.2 , pp. 173-182
    • Deng, W.1    Li, C.2    Guo, Q.3
  • 5
    • 33947133956 scopus 로고    scopus 로고
    • Stability analysis of linear fractional differential system with multiple time delays
    • W. H. Deng, C. P. Li, and J. H. Lü, "Stability analysis of linear fractional differential system with multiple time delays," Nonlinear Dynamics, Vol. 48, no. 4, pp. 409-416, 2007.
    • (2007) Nonlinear Dynamics , vol.48 , Issue.4 , pp. 409-416
    • Deng, W.H.1    Li, C.P.2    Lü, J.H.3
  • 6
    • 84885703806 scopus 로고    scopus 로고
    • LMI characterization of fractional systems stability
    • Springer, Dordrecht, The Netherlands
    • M. Moze, J. Sabatier, and A. Oustaloup, "LMI characterization of fractional systems stability," in Advances in Fractional Calculus, pp. 419-434, Springer, Dordrecht, The Netherlands, 2007.
    • (2007) Advances in Fractional Calculus , pp. 419-434
    • Moze, M.1    Sabatier, J.2    Oustaloup, A.3
  • 7
    • 77958144351 scopus 로고    scopus 로고
    • Stability analysis of the fractional differential systems with miller-ross sequential derivative
    • Jinan, China
    • D. L. Qian and C. P. Li, "Stability analysis of the fractional differential systems with Miller-Ross sequential derivative," in Proceedings of the 8th World Congress on Intelligent Control and Automation, pp. 213-219, Jinan, China, 2010.
    • (2010) Proceedings of the 8th World Congress on Intelligent Control and Automation , pp. 213-219
    • Qian, D.L.1    Li, C.P.2
  • 8
    • 77954177563 scopus 로고    scopus 로고
    • Stability analysis of fractional differential system with riemann-liouville derivative
    • D. L. Qian, C. P. Li, R. P. Agarwal, and P. J. Y. Wong, "Stability analysis of fractional differential system with Riemann-Liouville derivative," Mathematical and Computer Modelling, Vol. 52, no. 5-6, pp. 862-874, 2010.
    • (2010) Mathematical and Computer Modelling , vol.52 , Issue.5-6 , pp. 862-874
    • Qian, D.L.1    Li, C.P.2    Agarwal, R.P.3    Wong, P.J.Y.4
  • 9
    • 65549098895 scopus 로고    scopus 로고
    • On the stability of linear systems with fractional-order elements
    • A. G. Radwan, A. M. Soliman, A. S. Elwakil, and A. Sedeek, "On the stability of linear systems with fractional-order elements," Chaos, Solitons & Fractals, Vol. 40, no. 5, pp. 2317-2328, 2009.
    • (2009) Chaos, Solitons & Fractals , vol.40 , Issue.5 , pp. 2317-2328
    • Radwan, A.G.1    Soliman, A.M.2    Elwakil, A.S.3    Sedeek, A.4
  • 10
  • 11
    • 57649105528 scopus 로고    scopus 로고
    • A note on the stability of fractional order systems
    • M. S. Tavazoei and M. Haeri, "A note on the stability of fractional order systems," Mathematics and Computers in Simulation, Vol. 79, no. 5, pp. 1566-1576, 2009.
    • (2009) Mathematics and Computers in Simulation , vol.79 , Issue.5 , pp. 1566-1576
    • Tavazoei, M.S.1    Haeri, M.2
  • 12
    • 2442548776 scopus 로고    scopus 로고
    • Analysis of a system of fractional differential equations
    • DOI 10.1016/j.jmaa.2004.01.013
    • V. Daftardar-Gejji and A. Babakhani, "Analysis of a system of fractional differential equations," Journal of Mathematical Analysis and Applications, Vol. 293, no. 2, pp. 511-522, 2004. (Pubitemid 38613236)
    • (2004) Journal of Mathematical Analysis and Applications , vol.293 , Issue.2 , pp. 511-522
    • Daftardar-Gejji, V.1    Babakhani, A.2
  • 14
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-leffler stability of fractional order nonlinear dynamic systems
    • Y. Li, Y. Q. Chen, and I. Podlubny "Mittag-Leffler stability of fractional order nonlinear dynamic systems," Automatica, Vol. 45, no. 8, pp. 1965-1969, 2009.
    • (2009) Automatica , vol.45 , Issue.8 , pp. 1965-1969
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 15
    • 76449092011 scopus 로고    scopus 로고
    • Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized mittag-leffler stability
    • Y Li, Y Q. Chen, and I. Podlubny, "Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability," Computers & Mathematics with Applications, Vol. 59, no. 5, pp. 1810-1821, 2010.
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.5 , pp. 1810-1821
    • Li, Y.1    Chen, Y.Q.2    Podlubny, I.3
  • 16
    • 74149094877 scopus 로고    scopus 로고
    • Fractional integral inequalities and applications
    • Z. Denton and A. S. Vatsala, "Fractional integral inequalities and applications," Computers & Mathematics with Applications, Vol. 59, no. 3, pp. 1087-1094, 2010.
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.3 , pp. 1087-1094
    • Denton, Z.1    Vatsala, A.S.2
  • 17
    • 77956714938 scopus 로고    scopus 로고
    • Comparison theorems for fractional differential equations
    • (Chinese)
    • T. C. Hu, D. L. Qian, and C. P. Li, "Comparison theorems for fractional differential equations," Communication on Applied Mathematics and Computation, Vol. 23, no. 1, pp. 97-103, 2009 (Chinese).
    • (2009) Communication on Applied Mathematics and Computation , vol.23 , Issue.1 , pp. 97-103
    • Hu, T.C.1    Qian, D.L.2    Li, C.P.3
  • 18
    • 79953697124 scopus 로고    scopus 로고
    • Introduction to fractional integrability and differentiability
    • C. P. Li and Z. G. Zhao, "Introduction to fractional integrability and differentiability," European Physical Journal - Special Topics, Vol. 193, no. 1, pp. 5-26, 2011.
    • (2011) European Physical Journal - Special Topics , vol.193 , Issue.1 , pp. 5-26
    • Li, C.P.1    Zhao, Z.G.2
  • 19
    • 0013301123 scopus 로고
    • Peking University Press, Beijing, China
    • L. Huang, Stability Theory, Peking University Press, Beijing, China, 1992.
    • (1992) Stability Theory
    • Huang, L.1
  • 22
    • 0003797958 scopus 로고    scopus 로고
    • of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA
    • I. Podlubny, Fractional Differential Equations, Vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 23
    • 0346544234 scopus 로고    scopus 로고
    • A note on the complete monotonicity of the generalized mittag-leffler function
    • K. S. Miller and S. G. Samko, "A note on the complete monotonicity of the generalized Mittag-Leffler function," Real Analysis Exchange, Vol. 23, no. 2, pp. 753-755, 1997.
    • (1997) Real Analysis Exchange , vol.23 , Issue.2 , pp. 753-755
    • Miller, K.S.1    Samko, S.G.2
  • 24
    • 0345725424 scopus 로고    scopus 로고
    • Completely monotone generalized mittag-leffler functions
    • W. R. Schneider, "Completely monotone generalized Mittag-Leffler functions," Expositiones Mathe-maticae, Vol. 14, no. 1, pp. 3-16, 1996.
    • (1996) Expositiones Mathe-Maticae , vol.14 , Issue.1 , pp. 3-16
    • Schneider, W.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.