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Volumn 64, Issue 10, 2012, Pages 3389-3405

Nonlinear impulsive problems for fractional differential equations and Ulam stability

Author keywords

Boundary value problems; Cauchy problems; Fractional differential equations; Impulsive problems; Ulam stability

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; CAUCHY PROBLEMS; DATA DEPENDENCE; FIXED POINT THEOREMS; FRACTIONAL DIFFERENTIAL EQUATIONS; GRONWALL INEQUALITY; IMPULSIVE DIFFERENTIAL EQUATION; IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS; IMPULSIVE PROBLEMS; PIECEWISE-CONTINUOUS; ULAM STABILITY;

EID: 84865640170     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.02.021     Document Type: Article
Times cited : (206)

References (51)
  • 9
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • R.P. Agarwal, M. Benchohra, and S. Hamani A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta Appl. Math. 109 2010 973 1033
    • (2010) Acta Appl. Math. , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 10
    • 77956315480 scopus 로고    scopus 로고
    • Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory
    • B. Ahmad, and J.J. Nieto Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory Topol. Methods Nonlinear Anal. 35 2010 295 304
    • (2010) Topol. Methods Nonlinear Anal. , vol.35 , pp. 295-304
    • Ahmad, B.1    Nieto, J.J.2
  • 11
    • 71649083074 scopus 로고    scopus 로고
    • On positive solutions of a nonlocal fractional boundary value problem
    • Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. TMA 72 2010 916 924
    • (2010) Nonlinear Anal. TMA , vol.72 , pp. 916-924
    • Bai, Z.1
  • 12
    • 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
  • 13
    • 77049086990 scopus 로고    scopus 로고
    • Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay
    • G.M. Mophou, and G.M. N'Guérékata Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay Appl. Math. Comput. 216 2010 61 69
    • (2010) Appl. Math. Comput. , vol.216 , pp. 61-69
    • Mophou, G.M.1    N'Guérékata, G.M.2
  • 14
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • J. Wang, and Y. Zhou A class of fractional evolution equations and optimal controls Nonlinear Anal. RWA 12 2011 262 272
    • (2011) Nonlinear Anal. RWA , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 15
    • 79955979032 scopus 로고    scopus 로고
    • A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces
    • J. Wang, Y. Zhou, and W. Wei A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces Commun. Nonlinear Sci. Numer. Simul. 16 2011 4049 4059
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 4049-4059
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 16
    • 0037308989 scopus 로고    scopus 로고
    • Existence of positive solution for some class of nonlinear fractional differential equations
    • DOI 10.1016/S0022-247X(02)00583-8
    • S. Zhang Existence of positive solution for some class of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 136 148 (Pubitemid 36445950)
    • (2003) Journal of Mathematical Analysis and Applications , vol.278 , Issue.1 , pp. 136-148
    • Zhang, S.1
  • 17
    • 77955515765 scopus 로고    scopus 로고
    • Nonlocal Cauchy problem for fractional evolution equations
    • Y. Zhou, and F. Jiao Nonlocal Cauchy problem for fractional evolution equations Nonlinear Anal. RWA 11 2010 4465 4475
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 18
    • 67349086967 scopus 로고    scopus 로고
    • Existence and uniqueness for p-type fractional neutral differential equations
    • Y. Zhou, F. Jiao, and J. Li Existence and uniqueness for p-type fractional neutral differential equations Nonlinear Anal. TMA 71 2009 2724 2733
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 2724-2733
    • Zhou, Y.1    Jiao, F.2    Li, J.3
  • 19
    • 67349177003 scopus 로고    scopus 로고
    • Existence and uniqueness for fractional neutral differential equations with infinite delay
    • Y. Zhou, F. Jiao, and J. Li Existence and uniqueness for fractional neutral differential equations with infinite delay Nonlinear Anal. TMA 71 2009 3249 3256
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 3249-3256
    • Zhou, Y.1    Jiao, F.2    Li, J.3
  • 23
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • R.P. Agarwal, M. Benchohra, and S. Hamani A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta Appl. Math. 109 2010 973 1033
    • (2010) Acta Appl. Math. , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 24
    • 67549135865 scopus 로고    scopus 로고
    • Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations
    • B. Ahmad, and S. Sivasundaram Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations Nonlinear Anal. Hybrid Syst. 3 2009 251 258
    • (2009) Nonlinear Anal. Hybrid Syst. , vol.3 , pp. 251-258
    • Ahmad, B.1    Sivasundaram, S.2
  • 25
    • 85087244166 scopus 로고    scopus 로고
    • Impulsive fractional differential equations in Banach spaces
    • (Spec. Ed. I)
    • M. Benchohra, and D. Seba Impulsive fractional differential equations in Banach spaces Electron. J. Qual. Theory Differ. Equ. 2009 8 2009 e1 e14 (Spec. Ed. I)
    • (2009) Electron. J. Qual. Theory Differ. Equ. , vol.2009 , Issue.8
    • Benchohra, M.1    Seba, D.2
  • 26
    • 77950369747 scopus 로고    scopus 로고
    • Existence of solutions of abstract fractional impulsive semilinear evolution equations
    • K. Balachandran, and S. Kiruthika Existence of solutions of abstract fractional impulsive semilinear evolution equations Electron. J. Qual. Theory Differ. Equ. 2010 4 2010 e1 e12
    • (2010) Electron. J. Qual. Theory Differ. Equ. , vol.2010 , Issue.4
    • Balachandran, K.1    Kiruthika, S.2
  • 27
    • 78149285834 scopus 로고    scopus 로고
    • Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions
    • G. Wang, L. Zhang, and G. Song Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions Nonlinear Anal. TMA 74 2011 974 982
    • (2011) Nonlinear Anal. TMA , vol.74 , pp. 974-982
    • Wang, G.1    Zhang, L.2    Song, G.3
  • 28
    • 84856291615 scopus 로고    scopus 로고
    • On the concept and existence of solution for impulsive fractional differential equations
    • M. Feckan, Y. Zhou, and J. Wang On the concept and existence of solution for impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 17 2012 3050 3060
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 3050-3060
    • Feckan, M.1    Zhou, Y.2    Wang, J.3
  • 30
    • 0001260759 scopus 로고
    • On the stability of the linear functional equation
    • D.H. Hyers On the stability of the linear functional equation Proc. Natl. Acad. Sci. 27 1941 222 224
    • (1941) Proc. Natl. Acad. Sci. , vol.27 , pp. 222-224
    • Hyers, D.H.1
  • 31
    • 84966221118 scopus 로고
    • On the stability of linear mappings in Banach spaces
    • Th.M. Rassias On the stability of linear mappings in Banach spaces Proc. Amer. Math. Soc. 72 1978 297 300
    • (1978) Proc. Amer. Math. Soc. , vol.72 , pp. 297-300
    • Rassias, Th.M.1
  • 32
    • 84868199458 scopus 로고    scopus 로고
    • Stabilitatea Ulam-Hyers-Bourgin pentru ecuatii functionale
    • L. Cadariu Stabilitatea Ulam-Hyers-Bourgin pentru ecuatii functionale Ed. Univ. Vest Timişara, Timişara 2007
    • (2007) Ed. Univ. Vest Timişara, Timişara
    • Cadariu, L.1
  • 35
    • 10644290151 scopus 로고    scopus 로고
    • Hyers-Ulam stability of linear differential equations of first order
    • S.-M. Jung Hyers-Ulam stability of linear differential equations of first order Appl. Math. Lett. 17 2004 1135 1140
    • (2004) Appl. Math. Lett. , vol.17 , pp. 1135-1140
    • Jung, S.-M.1
  • 36
    • 0142087794 scopus 로고    scopus 로고
    • A characterization of Hyers-Ulam stability of first order linear differential operators
    • DOI 10.1016/S0022-247X(03)00458-X
    • T. Miura, S. Miyajima, and S.-E. Takahasi A characterization of Hyers-Ulam stability of first order linear differential operators J. Math. Anal. Appl. 286 2003 136 146 (Pubitemid 37282214)
    • (2003) Journal of Mathematical Analysis and Applications , vol.286 , Issue.1 , pp. 136-146
    • Miura, T.1    Miyajima, S.2    Takahasi, S.-E.3
  • 37
    • 0141865505 scopus 로고    scopus 로고
    • Hyers-Ulam stability of linear differential operator with constant coefficients
    • DOI 10.1002/mana.200310088
    • T. Miura, S. Miyajima, and S.-E. Takahasi Hyers-Ulam stability of linear differential operator with constant coefficients Math. Nachr. 258 2003 90 96 (Pubitemid 37177576)
    • (2003) Mathematische Nachrichten , vol.258 , pp. 90-96
    • Miura, T.1    Miyajima, S.2    Takahasi, S.-E.3
  • 38
    • 70350648459 scopus 로고    scopus 로고
    • Ulam stability of ordinary differential equations
    • I.A. Rus Ulam stability of ordinary differential equations Stud. Univ. "Babeş-Bolyai" Math. 54 2009 125 133
    • (2009) Stud. Univ. "babeş-Bolyai" Math. , vol.54 , pp. 125-133
    • Rus, I.A.1
  • 39
    • 55649110239 scopus 로고
    • Hyers stability of the linear differential equation
    • M. Oboza Hyers stability of the linear differential equation Rocznik Nauk.-Dydakt. Prace Mat. 13 1993 259 270
    • (1993) Rocznik Nauk.-Dydakt. Prace Mat. , vol.13 , pp. 259-270
    • Oboza, M.1
  • 40
    • 55649083686 scopus 로고    scopus 로고
    • Connections between Hyers and Lyapunov stability of the ordinary differential equations
    • M. Oboza Connections between Hyers and Lyapunov stability of the ordinary differential equations Rocznik Nauk.-Dydakt. Prace Mat. 14 1997 141 146
    • (1997) Rocznik Nauk.-Dydakt. Prace Mat. , vol.14 , pp. 141-146
    • Oboza, M.1
  • 42
    • 79956114935 scopus 로고    scopus 로고
    • Hyers-Ulam stability of Euler's equation
    • D.S. Cimpean, and D. Popa Hyers-Ulam stability of Euler's equation Appl. Math. Lett. 24 2011 1539 1543
    • (2011) Appl. Math. Lett. , vol.24 , pp. 1539-1543
    • Cimpean, D.S.1    Popa, D.2
  • 43
    • 80051799017 scopus 로고    scopus 로고
    • Hyers-Ulam stability of a first order partial differential equation
    • N. Lungu, and D. Popa Hyers-Ulam stability of a first order partial differential equation J. Math. Anal. Appl. 385 2012 86 91
    • (2012) J. Math. Anal. Appl. , vol.385 , pp. 86-91
    • Lungu, N.1    Popa, D.2
  • 44
    • 80053076876 scopus 로고    scopus 로고
    • Ulam stability and data dependence for fractional differential equations with Caputo derivative
    • J. Wang, L. Lv, and Y. Zhou Ulam stability and data dependence for fractional differential equations with Caputo derivative Electron. J. Qual. Theory Differ. Equ. 63 2011 1 10
    • (2011) Electron. J. Qual. Theory Differ. Equ. , vol.63 , pp. 1-10
    • Wang, J.1    Lv, L.2    Zhou, Y.3
  • 45
    • 84855222640 scopus 로고    scopus 로고
    • New concepts and results in stability of fractional differential equations
    • J. Wang, L. Lv, and Y. Zhou New concepts and results in stability of fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 17 2012 2530 2538
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 2530-2538
    • Wang, J.1    Lv, L.2    Zhou, Y.3
  • 46
    • 84855992801 scopus 로고    scopus 로고
    • Mittag-Leffler-Ulam stabilities of fractional evolution equations
    • J. Wang, and Y. Zhou Mittag-Leffler-Ulam stabilities of fractional evolution equations Appl. Math. Lett. 25 2012 723 728
    • (2012) Appl. Math. Lett. , vol.25 , pp. 723-728
    • Wang, J.1    Zhou, Y.2
  • 48
    • 33846028541 scopus 로고    scopus 로고
    • On a nonlinear integral equation without compactness
    • F. Isaia On a nonlinear integral equation without compactness Acta Math. Univ. Comenian. LXXV 2006 233 240
    • (2006) Acta Math. Univ. Comenian. , vol.75 , pp. 233-240
    • Isaia, F.1
  • 49
    • 33845882236 scopus 로고    scopus 로고
    • A generalized Gronwall inequality and its application to a fractional differential equation
    • H. Ye, J. Gao, and Y. Ding A generalized Gronwall inequality and its application to a fractional differential equation J. Math. Anal. Appl. 328 2007 1075 1081
    • (2007) J. Math. Anal. Appl. , vol.328 , pp. 1075-1081
    • Ye, H.1    Gao, J.2    Ding, Y.3
  • 50
    • 80355123583 scopus 로고    scopus 로고
    • Impulsive fractional evolution equations and optimal controls in infinite dimensional spaces
    • J. Wang, Y. Zhou, and W. Wei Impulsive fractional evolution equations and optimal controls in infinite dimensional spaces Topol. Methods Nonlinear Anal. 38 2011 17 43
    • (2011) Topol. Methods Nonlinear Anal. , vol.38 , pp. 17-43
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 51
    • 84855950961 scopus 로고    scopus 로고
    • Existence and uniqueness results for fractional differential equations with boundary value conditions
    • L. Lv, J. Wang, and W. Wei Existence and uniqueness results for fractional differential equations with boundary value conditions Opuscula Math. 31 2011 629 643
    • (2011) Opuscula Math. , vol.31 , pp. 629-643
    • Lv, L.1    Wang, J.2    Wei, W.3


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