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)
The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay. (English) Zbl 1207.34101
Summary: This paper is mainly concerned with the existence and uniqueness of mild solutions for systems of fractional impulsive neutral functional infinite delay integrodifferential equations with nonlocal initial conditions. The results are obtained using a fixed point theorem combined with a strongly continuous operator semigroup.

MSC:
34K37Functional-differential equations with fractional derivatives
34K30Functional-differential equations in abstract spaces
34K45Functional-differential equations with impulses
47N20Applications of operator theory to differential and integral equations
WorldCat.org
Full Text: DOI
References:
[1] Benchohra, Mouffak; Hamani, Samira: The method of upper and lower solutions and impulsive fractional differential inclusions, Nonlinear analysis: hybrid systems 3, 433-440 (2009) · Zbl 1221.49060 · doi:10.1016/j.nahs.2009.02.009
[2] Lakshmikantham, V.; Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear analysis. Theory methods and applications 69, No. 8, 2677-2682 (2008) · Zbl 1161.34001 · doi:10.1016/j.na.2007.08.042
[3] N’guérékata, G. M.: A Cauchy problem for some fractional abstract differential equation with nonlocal conditions, Nonlinear analysis. Theory methods and applications 70, No. 5, 1873-1876 (2009) · Zbl 1166.34320 · doi:10.1016/j.na.2008.02.087
[4] Belarbi, A.; Benchohra, M.; Ouahab, A.: Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. anal. 85, 1459-1470 (2006) · Zbl 1175.34080 · doi:10.1080/00036810601066350
[5] Lin, Wei: Global existence and chaos control of fractional differential equations, Journal of mathematical analysis and applications 332, 709-726 (2007) · Zbl 1113.37016 · doi:10.1016/j.jmaa.2006.10.040
[6] Mophou, G. M.; N’guérékata, G. M.: Existence of mild solution for some fractional differential equations with nonlocal conditions, Semigroup forum 79, No. 2, 322-335 (2009) · Zbl 1180.34006 · doi:10.1007/s00233-008-9117-x
[7] Lakshmikantham, V.: Theory of fractional differential equations, Nonlinear analysis. Theory methods and applications 60, No. 10, 3337-3343 (2008) · Zbl 1162.34344 · doi:10.1016/j.na.2007.09.025
[8] Benchohra, Mouffak; Berhoun, Farida: Impulsive fractional differential equations with variable times, Computers and mathematics with applications 59, 1245-1252 (2010) · Zbl 1189.34007 · doi:10.1016/j.camwa.2009.05.016
[9] Ahmad, Bashir; Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear analysis: hybrid systems 3, No. 3, 251-258 (2009) · Zbl 1193.34056 · doi:10.1016/j.nahs.2009.01.008
[10] Agarwal, R. P.; Benchohra, M.; Slimani, B. A.: Existence results for differential equations with fractional order and impulses, Memoirs on differential equations and mathemaical physics 44, 1-21 (2008) · Zbl 1178.26006
[11] Benchohra, M.; Slimani, B. A.: Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic journal of differential equations 10, 1-11 (2009) · Zbl 1178.34004 · emis:journals/EJDE/Volumes/2009/10/abstr.html
[12] Mophou, Gisèle M.: Existence and uniqueness of mild solutions to impulsive fractional differential equations, Nonlinear analysis 72, 1604-1615 (2010) · Zbl 1187.34108 · doi:10.1016/j.na.2009.08.046
[13] Sadovskii, B. N.: On a fixed point principle, Functional analysis and its applications 1, No. 2, 74-76 (1967)
[14] Chang, Y. K.: Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos, solitons and fractals 33, 1601-1609 (2007) · Zbl 1136.93006 · doi:10.1016/j.chaos.2006.03.006