zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the controllability of impulsive fractional evolution inclusions in Banach spaces. (English) Zbl 1263.93035
Summary: In this paper, we deal with the controllability of a class of impulsive fractional evolution inclusions in Banach spaces. We establish some sufficient conditions of controllability by use of the well-known fixed point theorem for multivalued maps due to Dhage associated with an evolution system. At the end of the paper, a concrete application is given to illustrate our main results.
MSC:
93B05Controllability
49J53Set-valued and variational analysis
26A33Fractional derivatives and integrals (real functions)
References:
[1]Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Math. Studies, vol. 204. Elsevier, Amsterdam (2006)
[2]Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
[3]Liu, Z.H., Sun, J.H.: Nonlinear boundary value problems of fractional differential systems. Comput. Appl. Math. 64, 463–475 (2012) · Zbl 1252.34006 · doi:10.1016/j.camwa.2011.12.020
[4]Liu, Z.H., Lu, L.: A class of BVPs for nonlinear fractional differential equations with p-Laplacian operator. Electron. J. Qual. Theory Differ. Equ. 70, 1–16 (2012) · doi:10.1186/1687-1847-2012-1
[5]Wang, J.R., Zhou, Y.: Completely controllability of fractional evolution systems. Commun. Nonlinear Sci. Numer. Simul. 17, 4346–4355 (2012) · Zbl 1248.93029 · doi:10.1016/j.cnsns.2012.02.029
[6]Abada, N., Benchohra, M., Hammouche, H.: Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions. J. Differ. Equ. 246, 3834–3863 (2009) · Zbl 1171.34052 · doi:10.1016/j.jde.2009.03.004
[7]Liu, Z.H., Han, J.F., Fang, L.J.: Integral boundary value problems for first order integro-differential equations with impulsive integral conditions. Comput. Appl. Math. 61, 3035–3043 (2011) · Zbl 1222.45006 · doi:10.1016/j.camwa.2011.03.094
[8]Liu, Z.H., Liang, J.T.: A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments. J. Comput. Appl. Math. 237, 477–486 (2013) · Zbl 1259.45008 · doi:10.1016/j.cam.2012.06.018
[9]Wang, J.R., Feckan, M., Zhou, Y.: On the new concept of solutions and existence results for impulsive fractional evolution equations. Dyn. Partial Differ. Equ. 8(4), 345–361 (2011) · doi:10.4310/DPDE.2011.v8.n4.a3
[10]Dhage, B.C.: Multi-valued mappings and fixed points II. Tamkang J. Math. 37(1), 27–46 (2006)
[11]Hu, S.C., Papageorgiou, N.S.: Handbook of Multivalued Analysis (Theory). Kluwer Academic, Dordrecht (1997)
[12]Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)
[13]Zhou, Y., Jiao, F.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59, 1063–1077 (2010) · Zbl 1189.34154 · doi:10.1016/j.camwa.2009.06.026
[14]Lasota, A., Opial, Z.: An application of the Kakutani–KY–Fan theorem in the theory of ordinary differential equations. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 13, 781–786 (1965)
[15]Ye, H.P., Gao, J.M., Ding, Y.S.: A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328, 1075–1081 (2007) · Zbl 1120.26003 · doi:10.1016/j.jmaa.2006.05.061