메뉴 건너뛰기




Volumn 41, Issue 1, 2013, Pages 113-133

Existence and stability of fractional differential equations with Hadamard derivative

Author keywords

Blowing up solutions; Existence; Fractional differential equations; Hadamard derivative; Nonlinear integral inequality; Ulam hyers stability

Indexed keywords


EID: 84888252353     PISSN: 12303429     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (76)

References (39)
  • 1
    • 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
  • 2
    • 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
  • 4
    • 71649083074 scopus 로고    scopus 로고
    • On positive solutions of a nonlocal fractional boundary value problem
    • Z.B. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal. 72 (2010), 916-924.
    • (2010) Nonlinear Anal , vol.72 , pp. 916-924
    • Bai, Z.B.1
  • 5
    • 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
  • 6
    • 3042938751 scopus 로고
    • A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations
    • G. Butler and T. Rogers, A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations, J. Math. Anal. Appl. 33 (1971), 77-81.
    • (1971) J. Math. Anal. Appl , vol.33 , pp. 77-81
    • Butler, G.1    Rogers, T.2
  • 8
    • 68349100153 scopus 로고    scopus 로고
    • Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order
    • Y.-K. Chang, V. Kavitha and M. Mallika Arjunanb, Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order, Nonlinear Anal. 71 (2009), 5551-5559.
    • (2009) Nonlinear Anal , vol.71 , pp. 5551-5559
    • Chang, Y.-K.1    Kavitha, V.2    Mallika Arjunanb, M.3
  • 11
    • 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
    • 33847309315 scopus 로고    scopus 로고
    • Theory and applications of fractional differential equations
    • North-Holland, Elsevier Science B.V., Amsterdam
    • A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Mathematics Studies, vol. 204, North-Holland, Elsevier Science B.V., Amsterdam, 2006.
    • (2006) Mathematics Studies , vol.204
    • Kilbas, A.A.1    Srivastava, H.M.2    Trujillo, J.J.3
  • 18
    • 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
  • 19
    • 76449092011 scopus 로고    scopus 로고
    • Stability of fractional-order nonlinear dynamic systems: Lyapunov direct me thod and generalized Mittag-Leffler stability
    • Y. Li, Y. Chen and I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct me thod 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
  • 20
    • 0031247674 scopus 로고    scopus 로고
    • A new approach to an analysis of Henry type integral inequalities and their Bihari type versions
    • M. Medveď, A new approach to an analysis of Henry type integral inequalities and their Bihari type versions, J. Math. Anal. Appl. 214 (1997), 349-366.
    • (1997) J. Math. Anal. Appl , vol.214 , pp. 349-366
    • Medveď, M.1
  • 21
    • 0037087657 scopus 로고    scopus 로고
    • Integral inequalities and global solutions of semilinear evolution equations
    • M. Medveď, Integral inequalities and global solutions of semilinear evolution equations, J. Math. Anal. Appl. 267 (2002), 643-650.
    • (2002) J. Math. Anal. Appl , vol.267 , pp. 643-650
    • Medveď, M.1
  • 22
    • 55849152794 scopus 로고    scopus 로고
    • Singular integral inequalities with several nonlinearities and integral equations with singular kernels
    • M. Medveď, Singular integral inequalities with several nonlinearities and integral equations with singular kernels, Nonlinear Oscil. 11 (2007), 70-79.
    • (2007) Nonlinear Oscil , vol.11 , pp. 70-79
    • Medveď, M.1
  • 23
    • 79955776995 scopus 로고    scopus 로고
    • Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices
    • M. Medveď, M. Pospíšil and L. Skripková, Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices, Nonlinear Anal. 74 (2011), 3903-3911.
    • (2011) Nonlinear Anal , vol.74 , pp. 3903-3911
    • Medveď, M.1    Pospíšil, M.2    Skripková, L.3
  • 25
    • 77049086990 scopus 로고    scopus 로고
    • Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay
    • G. M. Mophou, G.M. N'Gúeŕekata, 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'Gúeŕekata, G.M.2
  • 29
    • 70350648459 scopus 로고    scopus 로고
    • Ulam stability of ordinary differential equations
    • I.A. Rus, Ulam stability of ordinary differential equations, Studia Univ. Babes-Bolyai Math. 54 (2009), 125-133.
    • (2009) Studia Univ. Babes-Bolyai Math , vol.54 , pp. 125-133
    • Rus, I.A.1
  • 31
    • 80053076876 scopus 로고    scopus 로고
    • Ulam stability and data dependence for fractional differential equations with Caputo derivative
    • J. Wang and L. Lv and Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, E.J. Qualitative Theory of Differential Equations 2011, no. 63, e1-e10.
    • (2011) E.J. Qualitative Theory of Differential Equations , vol.63
    • Wang, J.1    Lv, L.2    Zhou, Y.3
  • 32
    • 84855222640 scopus 로고    scopus 로고
    • New concepts and results in stability of fractional differential equations
    • doi:10.1016/j.cnsns.2011.09.030
    • J. Wang and L. Lv and Y. Zhou, New concepts and results in stability of fractional differential equations, Com-mun. Nonlinear Sci. Numer. Simulat. (2011), doi:10.1016/j.cnsns.2011.09.030.
    • (2011) Com-mun. Nonlinear Sci. Numer. Simulat
    • Wang, J.1    Lv, L.2    Zhou, Y.3
  • 33
    • 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. 12 (2011), 262-272.
    • (2011) Nonlinear Anal , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 34
    • 80051576826 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional control systems in Banach spaces
    • J. Wang and Y. Zhou, Analysis of nonlinear fractional control systems in Banach spaces, Nonlinear Anal. 74 (2011), 5929-5942.
    • (2011) Nonlinear Anal , vol.74 , pp. 5929-5942
    • Wang, J.1    Zhou, Y.2
  • 35
    • 80052035803 scopus 로고    scopus 로고
    • Existence and controllability results for fractional semilinear differential inclu-sions
    • J. Wang and Y. Zhou, Existence and controllability results for fractional semilinear differential inclu-sions, Nonlinear Anal. 12 (2011), 3642-3653.
    • (2011) Nonlinear Anal , vol.12 , pp. 3642-3653
    • Wang, J.1    Zhou, Y.2
  • 36
    • 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
  • 37
    • 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. 11 (2010), 4465-4475.
    • (2010) Nonlinear Anal , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 38
    • 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. 71 (2009), 2724-2733.
    • (2009) Nonlinear Anal , vol.71 , pp. 2724-2733
    • Zhou, Y.1    Jiao, F.2    Li, J.3
  • 39
    • 67349177003 scopus 로고    scopus 로고
    • Existence and uniqueness for fractional neutral differential equations with in- finite delay
    • Y. Zhou, F. Jiao and J. Li, Existence and uniqueness for fractional neutral differential equations with in- finite 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.