Mild solution of fractional order differential equations with not instantaneous impulses
Open Mathematics (2015)
- Volume: 13, Issue: 1
- ISSN: 2391-5455
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topPei-Luan Li, and Chang-Jin Xu. "Mild solution of fractional order differential equations with not instantaneous impulses." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/271049>.
@article{Pei2015,
abstract = {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.},
author = {Pei-Luan Li, Chang-Jin Xu},
journal = {Open Mathematics},
keywords = {Mild solution; Fractional order; Not instantaneous impulse},
language = {eng},
number = {1},
pages = {null},
title = {Mild solution of fractional order differential equations with not instantaneous impulses},
url = {http://eudml.org/doc/271049},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Pei-Luan Li
AU - Chang-Jin Xu
TI - Mild solution of fractional order differential equations with not instantaneous impulses
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Mild solution; Fractional order; Not instantaneous impulse
UR - http://eudml.org/doc/271049
ER -
References
top- [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 Banach spaces, Appl. Math. Lett., 2009, 22 (11), 1760–1765 [Crossref] Zbl1181.34078
- [3] Shu X., Lai Y., Chen Y., The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal., 2011, 74, 2003–2011 Zbl1227.34009
- [4] Zhang X., Huang X., Liu Z., The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay, Nonlinear Anal. Hybrid Syst., 2010, 4 , 775–781 [WoS] Zbl1207.34101
- [5] Hernandez E., O’Regan D., On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 2013, 141, 1641– 1649 Zbl1266.34101
- [6] Pierri M., O’Regan D., Rolnik V., Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses, Appl. Math. Comput., 2013, 219, 6743–6749 Zbl1293.34019
- [7] Zhou Y., Jiao F.,Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal: RWA, 2010, 11, 4465–4475 Zbl1260.34017
- [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 Zbl1177.34084
- [9] Diethelm K., The analysis of fractional differential equations, Lect. Notes Math., 2010 [Crossref] Zbl1215.34001
- [10] Kilbas A.A., Srivastava M.H., Trujillo J.J., Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics 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 Zbl1188.37002
- [12] Miller K.S., Ross B., An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993 Zbl0789.26002
- [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 fractional differential equations and inclusions, Acta. Appl. Math., 2010, 109, 973–1033 [WoS] Zbl1198.26004
- [16] Benchohra M., Henderson J., Ntouyas S.K., Ouahab A., Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 2008,338,1340–1350 Zbl1209.34096
- [17] Wang J., Zhou Y.,A class of fractional evolution equations and optimal controls, Nonlinear Anal: RWA., 2011,12, 262–272 Zbl1214.34010
- [18] Wang J., Zhou Y., Wei W.,A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces, Commun Nonlinear Sci Numer Simulat, 2011, 16 , 4049–4059 [WoS][Crossref] Zbl1223.45007
- [19] Zhang S., Existence of positive solution for some class of nonlinear fractional differential equations, J. Math. Anal. Appl., 2003, 278, 136–148 Zbl1026.34008
- [20] Guo T., Jiang W., Impulsive problems for fractional differential equations with boundary valueconditions, Comput. Math. Appl., 2012, 64 , 3281–3291 [Crossref] Zbl1268.34014
- [21] Krasnoselskii Ma., Topological methods in the theory of nonlinear integral equation., Pergamon Press, New York, 1964
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