zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Approximate controllability of fractional neutral stochastic system with infinite delay. (English) Zbl 1263.93039
Summary: The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii’s fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
34K37Functional-differential equations with fractional derivatives
34K50Stochastic functional-differential equations
60G22Fractional processes, including fractional Brownian motion
60H15Stochastic partial differential equations