메뉴 건너뛰기




Volumn 247, Issue , 2014, Pages 72-89

On the concept of general solution for impulsive differential equations of fractional order q∈ (0, 1)

Author keywords

Existence; Fractional differential equations; Impulse General solution; Impulsive fractional differential equations

Indexed keywords

EXISTENCE; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER; GENERAL SOLUTIONS; IMPULSIVE DIFFERENTIAL EQUATION; IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS;

EID: 84907540956     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.08.069     Document Type: Article
Times cited : (33)

References (26)
  • 3
    • 77956684069 scopus 로고    scopus 로고
    • Theory and applications of fractional differential equations
    • Elsevier Science Amsterdam
    • A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations North-Holland Mathematics Studies vol. 204 2006 Elsevier Science Amsterdam
    • (2006) North-Holland Mathematics Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 6
    • 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.: Real World Appl. 11 2010 4465 4475
    • (2010) Nonlinear Anal.: Real World Appl. , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 7
    • 74149093181 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional neutral evolution equations
    • Y. Zhou, and F. Jiao Existence of mild solutions for fractional neutral evolution equations Comput. Math. Appl. 59 2010 1063 1077
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1063-1077
    • Zhou, Y.1    Jiao, F.2
  • 8
    • 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
  • 9
    • 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
  • 10
    • 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
  • 11
    • 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
  • 12
    • 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    Nguérékata, G.M.2
  • 13
    • 0037308989 scopus 로고    scopus 로고
    • Existence of positive solution for some class of nonlinear fractional differential equations
    • S. Zhang Existence of positive solution for some class of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 136 148
    • (2003) J. Math. Anal. Appl. , vol.278 , pp. 136-148
    • Zhang, S.1
  • 14
    • 67651103488 scopus 로고    scopus 로고
    • Existence results for differential equations with fractional order and impulses
    • R.P. Agarwal, M. Benchohra, and B.A. Slimani Existence results for differential equations with fractional order and impulses Mem. Differ. Equ. Math. Phys. 44 2008 1 21
    • (2008) Mem. Differ. Equ. Math. Phys. , vol.44 , pp. 1-21
    • Agarwal, R.P.1    Benchohra, M.2    Slimani, B.A.3
  • 15
    • 84856291615 scopus 로고    scopus 로고
    • On the concept and existence of solution for impulsive fractional differential equations
    • M. Feckan, Y. Zhou, and J.R. 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.R.3
  • 16
    • 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
  • 17
    • 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
  • 18
    • 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. 4 2010 1 12
    • (2010) Electron. J. Qual. Theory Differ. Equ. , vol.4 , pp. 1-12
    • Balachandran, K.1    Kiruthika, S.2
  • 19
    • 85087244166 scopus 로고    scopus 로고
    • Impulsive fractional differential equations in Banach spaces
    • (Special Edition I)
    • M. Benchohra, and D. Seba Impulsive fractional differential equations in Banach spaces Electron. J. Qual. Theory Differ. Equ. 8 2009 1 14 (Special Edition I)
    • (2009) Electron. J. Qual. Theory Differ. Equ. , Issue.8 , pp. 1-14
    • Benchohra, M.1    Seba, D.2
  • 20
    • 84868206100 scopus 로고    scopus 로고
    • On recent developments in the theory of boundary value problems for impulsive fractional differential equations
    • J.R. Wang, Y. Zhou, and M. Feckan On recent developments in the theory of boundary value problems for impulsive fractional differential equations Comput. Math. Appl. 64 2012 3008 3020
    • (2012) Comput. Math. Appl. , vol.64 , pp. 3008-3020
    • Wang, J.R.1    Zhou, Y.2    Feckan, M.3
  • 21
    • 84861670221 scopus 로고    scopus 로고
    • On the natural solution of an impulsive fractional differential equation of order q (1, 2)
    • J.R. Wang, X. Li, and W. Wei On the natural solution of an impulsive fractional differential equation of order q (1, 2) Commun. Nonlinear Sci. Numer. Simul. 17 2012 4384 4394
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 4384-4394
    • Wang, J.R.1    Li, X.2    Wei, W.3
  • 22
    • 84885190980 scopus 로고    scopus 로고
    • Comments on the concept of existence of solution for impulsive fractional differential equations
    • G. Wang, B. Ahmad, L. Zhang, and J.J. Nieto Comments on the concept of existence of solution for impulsive fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 19 12 2014 401 403
    • (2014) Commun. Nonlinear Sci. Numer. Simul. , vol.19 , Issue.12 , pp. 401-403
    • Wang, G.1    Ahmad, B.2    Zhang, L.3    Nieto, J.J.4
  • 23
    • 84901934110 scopus 로고    scopus 로고
    • Response to "comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:401-3.]"
    • M. Feckan, Y. Zhou, and J.R. Wang Response to "Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:401-3.]" Commun. Nonlinear Sci. Numer. Simul. 19 12 2014 4213 4215
    • (2014) Commun. Nonlinear Sci. Numer. Simul. , vol.19 , Issue.12 , pp. 4213-4215
    • Feckan, M.1    Zhou, Y.2    Wang, J.R.3
  • 24
    • 68949176622 scopus 로고    scopus 로고
    • The method of upper and lower solutions and impulsive fractional differential inclusions
    • Mouffak Benchohra, and Samira Hamani The method of upper and lower solutions and impulsive fractional differential inclusions Nonlinear Anal.: Hybrid Syst. 3 2009 433 440
    • (2009) Nonlinear Anal.: Hybrid Syst. , vol.3 , pp. 433-440
    • Benchohra, M.1    Hamani, S.2
  • 25
    • 78651363714 scopus 로고    scopus 로고
    • The existence of mild solutions for impulsive fractional partial differential equations
    • Xiao-Bao Shu, Yongzeng Lai, and Yuming Chen The existence of mild solutions for impulsive fractional partial differential equations Nonlinear Anal. 74 2011 2003 2011
    • (2011) Nonlinear Anal. , vol.74 , pp. 2003-2011
    • Shu, X.-B.1    Lai, Y.2    Chen, Y.3
  • 26


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.