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Volumn , Issue , 2011, Pages 1-18

Fixed points and asymptotic stability of nonlinear fractional difference equations

Author keywords

Asymptotic stability; Caputo like difference; Discrete Arzela Ascoli's theorem; Fractional difference equation; Schauder fixed point theorem

Indexed keywords


EID: 79958825483     PISSN: None     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2011.1.39     Document Type: Article
Times cited : (41)

References (31)
  • 1
    • 73249139676 scopus 로고    scopus 로고
    • On the concept of solution for fractional differential equations with uncertainty
    • R. P. Agarwal, V. Lakshmikantham, J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal. 72(2009) 2859-2862.
    • (2009) Nonlinear Anal , vol.72 , pp. 2859-2862
    • Agarwal, R.P.1    Lakshmikantham, V.2    Nieto, J.J.3
  • 3
    • 74149083825 scopus 로고    scopus 로고
    • Initial value problems in discrete fractional calculus
    • F. M. Atici, P. W. Eloe, Initial value problems in discrete fractional calculus, Proc. Amer. Math. Soc. 137(2009) 981-989.
    • (2009) Proc. Amer. Math. Soc , vol.137 , pp. 981-989
    • Atici, F.M.1    Eloe, P.W.2
  • 4
    • 77950548183 scopus 로고    scopus 로고
    • A transform method in discrete fractional calculus, Intern
    • F. M. Atici, P. W. Eloe, A transform method in discrete fractional calculus, Intern. J. Difference Equ. 2(2007) 165-176.
    • (2007) J. Difference Equ , vol.2 , pp. 165-176
    • Atici, F.M.1    Eloe, P.W.2
  • 6
    • 77952557731 scopus 로고    scopus 로고
    • Modeling with fractional difference equations
    • F. M. Atici, S. Seng̈ul, Modeling with fractional difference equations, J. Math. Anal. Appl. 369(2010) 1-9.
    • (2010) J. Math. Anal. Appl , vol.369 , pp. 1-9
    • Atici, F.M.1    Seng̈ul, S.2
  • 7
    • 34848916710 scopus 로고    scopus 로고
    • Existence results for fractional order functional differential equations with infinite delay
    • M. Benchohra, J. Henderson, S. K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338(2008) 1340-1350.
    • (2008) J. Math. Anal. Appl , vol.338 , pp. 1340-1350
    • Benchohra, M.1    Henderson, J.2    Ntouyas, S.K.3    Ouahab, A.4
  • 8
    • 0036568039 scopus 로고    scopus 로고
    • Krasnoselskii's fixed point theorem and stability
    • T. A. Burton, T. Furumochi, Krasnoselskii's fixed point theorem and stability, Nonlinear Anal. 49(2002) 445-454.
    • (2002) Nonlinear Anal , vol.49 , pp. 445-454
    • Burton, T.A.1    Furumochi, T.2
  • 9
    • 14944366448 scopus 로고    scopus 로고
    • Fixed points, stability, and exact linearization
    • T. A. Burton, Fixed points, stability, and exact linearization, Nonlinear Anal. 61(2005) 857-870.
    • (2005) Nonlinear Anal , vol.61 , pp. 857-870
    • Burton, T.A.1
  • 11
    • 79958860387 scopus 로고    scopus 로고
    • On the solutions for impulsive fractional functional differential equations
    • F. Chen, A. Chen, X. Wang, On the solutions for impulsive fractional functional differential equations, Diff. Equ. Dynam. Syst. 17(2009) 379-391.
    • (2009) Diff. Equ. Dynam. Syst , vol.17 , pp. 379-391
    • Chen, F.1    Chen, A.2    Wang, X.3
  • 13
    • 79958847070 scopus 로고    scopus 로고
    • Attractivity of fractional functional differential equations
    • doi: 10.1016/j.camwa.2011.03.062
    • F. Chen, Y. Zhou, Attractivity of fractional functional differential equations, Comput. Math. Appl. (2011), doi: 10.1016/j.camwa.2011.03.062.
    • (2011) Comput. Math. Appl
    • Chen, F.1    Zhou, Y.2
  • 14
    • 0000478105 scopus 로고
    • An existence theorem for a nonlinear difference equation
    • S. S. Cheng, W. T. Patula, An existence theorem for a nonlinear difference equation, Nonlinear Anal. 20(1993) 193-203.
    • (1993) Nonlinear Anal , vol.20 , pp. 193-203
    • Cheng, S.S.1    Patula, W.T.2
  • 15
    • 71549156256 scopus 로고    scopus 로고
    • Smoothness and stability of the solutions for nonlinear fractional differential equations
    • W. Deng, Smoothness and stability of the solutions for nonlinear fractional differential equations, Nonlinear Anal. 72(2010) 1768-1777.
    • (2010) Nonlinear Anal , vol.72 , pp. 1768-1777
    • Deng, W.1
  • 16
    • 59849106370 scopus 로고    scopus 로고
    • Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem
    • B. C. Dhage, Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem, Nonlinear Anal. 70(2009) 2485-2493.
    • (2009) Nonlinear Anal , vol.70 , pp. 2485-2493
    • Dhage, B.C.1
  • 17
    • 41749117533 scopus 로고    scopus 로고
    • Stability in functional differential equations established using fixed point theory
    • C. Jin, J. Luo, Stability in functional differential equations established using fixed point theory, Nonlinear Anal. 68(2008) 3307-3315.
    • (2008) Nonlinear Anal , vol.68 , pp. 3307-3315
    • Jin, C.1    Luo, J.2
  • 18
    • 77956684069 scopus 로고    scopus 로고
    • Theory and Applications of Fractional Differential Equations
    • Elsevier Science B.V., Amsterdam
    • A. A. Kilbas, Hari M. Srivastava, Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
    • (2006) North-Holland Mathematics Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 19
    • 51349139941 scopus 로고    scopus 로고
    • Theory of fractional functional differential equations
    • V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. 69(2008) 3337-3343.
    • (2008) Nonlinear Anal , vol.69 , pp. 3337-3343
    • Lakshmikantham, V.1
  • 21
    • 67649626081 scopus 로고    scopus 로고
    • Mittag-Leffler stability of fractional order nonlinear dynamic systems
    • Y. Li, Y. Chen, 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
  • 22
    • 76449092011 scopus 로고    scopus 로고
    • Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
    • Y. Li, Y. Chen, I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Comput. Math. Appl. 59(2010) 1810-1821.
    • (2010) Comput. Math. Appl , vol.59 , pp. 1810-1821
    • Li, Y.1    Chen, Y.2    Podlubny, I.3
  • 24
    • 77955429536 scopus 로고    scopus 로고
    • Maximum principles for fractional differential equations derived from Mittag-Leffler functions
    • J. J. Nieto, Maximum principles for fractional differential equations derived from Mittag-Leffler functions, Appl. Math. Lett. 23(2010) 1248-1251.
    • (2010) Appl. Math. Lett , vol.23 , pp. 1248-1251
    • Nieto, J.J.1
  • 26
    • 14944338681 scopus 로고    scopus 로고
    • Stability in neutral nonlinear differential equations with functional delays using fixed-point theory
    • Y. N. Raffoul, Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Math. Comput. Modelling 44(2004) 691-700.
    • (2004) Math. Comput. Modelling , vol.44 , pp. 691-700
    • Raffoul, Y.N.1
  • 27
    • 76649139783 scopus 로고    scopus 로고
    • LMI stability conditions for fractional order systems
    • J. Sabatier, M. Moze, C. Farges, LMI stability conditions for fractional order systems, Comput. Math. Appl. 59(2010) 1594-1609.
    • (2010) Comput. Math. Appl , vol.59 , pp. 1594-1609
    • Sabatier, J.1    Moze, M.2    Farges, C.3
  • 28
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • J. Wang, Y. Zhou, A class of fractional evolution equations and optimal controls. Nonlinear Anal.: Real World Applications 12(2011) 262-272.
    • (2011) Nonlinear Anal.: Real World Applications , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 30
    • 67349086967 scopus 로고    scopus 로고
    • Existence and uniqueness for p-type fractional neutral differential equations
    • Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for p-type fractional neutral differential equations, Nonlinear Anal. 71(2009) 2724-2733.
    • (2009) Nonlinear Anal , vol.71 , pp. 2724-2733
    • Zhou, Y.1    Jiao, F.2    Li, J.3
  • 31
    • 67349177003 scopus 로고    scopus 로고
    • Existence and uniqueness for fractional neutral differential equations with infinite delay
    • Y. Zhou, F. Jiao, J. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Anal. 71(2009) 3249-3256.
    • (2009) Nonlinear Anal , vol.71 , pp. 3249-3256
    • Zhou, Y.1    Jiao, F.2    Li, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.