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On nonlocal problems for fractional differential equations in Banach spaces

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Języki publikacji
EN
Abstrakty
EN
In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Rocznik
Strony
341--357
Opis fizyczny
Bibliogr. 24 poz.
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autor
autor
  • Guizhou University Department of Mathematics Guiyang, Guizhou 550025, P.R. China, jzdxw@yahoo.com.cn
Bibliografia
  • [1] L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494–505.
  • [2] L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991), 11–19.
  • [3] K. Balachandran, J.Y. Park, Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Anal. 71 (2009), 4471–4475.
  • [4] K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence results for fractional impulsive integrodifferential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 1970–1977.
  • [5] K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), 630–637.
  • [6] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, [in:] North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
  • [7] V. Lakshmikantham, S. Leela, J.V. Devi, Theory of fractional dynamic systems, Cambridge Scientific Publishers, 2009.
  • [8] K.S. Miller, B. Ross, An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993.
  • [9] G.M. N’Guérékata, A Cauchy problem for some fractional differential abstract differential equation with nonlocal conditions, Nonlinear Anal. 70 (2009), 1873–1876.
  • [10] G.M. N’Guérékata, Corrigendum: A Cauchy problem for some fractional differential equations, Commun. Math. Anal. 7 (2009), 11–11.
  • [11] G.M. Mophou, 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.
  • [12] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
  • [13] JinRong Wang, W. Wei, Y. Yang, Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control, Opuscula Math. 30 (2010), 217–234.
  • [14] JinRong Wang, Y. Yang, W. Wei, Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces, Opuscula Math. 30 (2010), 361–381.
  • [15] JinRong Wang, W. Wei, Y. Yang, On some impulsive fractional differential equations in Banach spaces, Opuscula Math. 30 (2010), 507–525.
  • [16] JinRong Wang, W. Wei, Y. Yang, Fractional nonlocal integrodifferential equations and its optimal control in Banach spaces, J. KSIAM 14 (2010), 79–91.
  • [17] JinRong Wang, Yong Zhou, Time optimal control problem of a class of fractional distributed systems, Int. J. Dyn. Diff. Eq. 3 (2011), in press.
  • [18] JinRong Wang, Yong Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal. 12 (2011), 262–272.
  • [19] JinRong Wang, X. Yan, X.-H. Zhang, T.-M. Wang, X.-Z. Li, A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions, Opuscula Math. 31 (2011), 119–135.
  • [20] JinRong Wang, W. Wei, Yong Zhou, Fractional finite time delay evolution systems and optimal controls in infinite dimensional spaces, J. Dyn. Contr. Syst. 17 (2011), in press.
  • [21] H. Ye, J. Gao, Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation, J. Math. Anal. Appl. 328 (2007), 1075–1081.
  • [22] Yong Zhou, Existence and uniqueness of fractional functional differential equations with unbounded delay, Int. J. Dyn. Diff. Eq. 1 (2008), 239–244.
  • [23] Yong Zhou, Feng Jiao, Existence of mild solutions for fractional neutral evolution equations, Comp. Math. Appl. 59 (2010), 1063–1077.
  • [24] Yong Zhou, Feng Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal. 11 (2010), 4465–4475.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0005-0063
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