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2015 | 13 | 1 |
Tytuł artykułu

Mild solution of fractional order differential equations with not instantaneous impulses

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-17
zaakceptowano
2015-06-29
online
2015-07-23
Twórcy
autor
  • School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang,
    471023, Henan, China
autor
  • Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Financeand Economics, Guiyang,
    550004, Guizhou, China
Bibliografia
  • [1] Mophou G. M., Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear Anal., 2010,72(3-4), 1604–1615
  • [2] Tai Z., Wang X., Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banachspaces, Appl. Math. Lett., 2009, 22 (11), 1760–1765[Crossref]
  • [3] Shu X., Lai Y., Chen Y., The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal., 2011,74, 2003–2011
  • [4] Zhang X., Huang X., Liu Z., The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocalconditions and infinite delay, Nonlinear Anal. Hybrid Syst., 2010, 4 , 775–781[WoS]
  • [5] Hernandez E., O’Regan D., On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 2013, 141, 1641–1649
  • [6] Pierri M., O’Regan D., Rolnik V., Existence of solutions for semi-linear abstract differential equations with not instantaneousimpulses, Appl. Math. Comput., 2013, 219, 6743–6749
  • [7] Zhou Y., Jiao F.,Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal: RWA, 2010, 11, 4465–4475
  • [8] Zhou Y., Jiao F., Li J., Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Anal:TMA., 2009,7, 3249–3256
  • [9] Diethelm K., The analysis of fractional differential equations, Lect. Notes Math., 2010[Crossref]
  • [10] Kilbas A.A., Srivastava M.H., Trujillo J.J., Theory and Applications of Fractional Differential Equations, in: North-HollandMathematics studies, vol.204, Elsevier Science B.V., Amsterdam, 2006
  • [11] Lakshmikantham V., Leela S., Vasundhara Devi J., Theory of fractional dynamic systems, Cambridge Scientific Publishers,Cambridge, 2009
  • [12] Miller K.S., Ross B., An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993
  • [13] Podlubny I., Fractional differential equations,. Academic Press, New York, 1999
  • [14] Tarasov VE., Fractional dynamics: application of fractional calculus to dynamics of particles, fields and media, Springer, HEP,2011
  • [15] Agarwal R. P., Benchohra M., Hamani S.,A survey on existence results for boundary valueproblems of nonlinear fractionaldifferential equations and inclusions, Acta. Appl. Math., 2010, 109, 973–1033[WoS]
  • [16] Benchohra M., Henderson J., Ntouyas S.K., Ouahab A., Existence results for fractional order functional differential equations withinfinite delay, J. Math. Anal. Appl., 2008,338,1340–1350
  • [17] Wang J., Zhou Y.,A class of fractional evolution equations and optimal controls, Nonlinear Anal: RWA., 2011,12, 262–272
  • [18] Wang J., Zhou Y., Wei W.,A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces, CommunNonlinear Sci Numer Simulat, 2011, 16 , 4049–4059[WoS][Crossref]
  • [19] Zhang S., Existence of positive solution for some class of nonlinear fractional differential equations, J. Math. Anal. Appl., 2003,278, 136–148
  • [20] Guo T., Jiang W., Impulsive problems for fractional differential equations with boundary valueconditions, Comput. Math. Appl.,2012, 64 , 3281–3291[Crossref]
  • [21] Krasnoselskii Ma., Topological methods in the theory of nonlinear integral equation., Pergamon Press, New York, 1964
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0042
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