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)
Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order. (English) Zbl 1179.45010

The paper deals with the existence and uniqueness of mild solutions to a semilinear integro-differential equation of fractional order. The problem studied here is:

D q x(t)+Ax(t)=ft,x(t), 0 t e(t,s,x(s))ds,t[0,a],x(0)+g(x)=x 0 ,

where 0<q<1, -A is the infinitesimal generator of a noncompact and analytic semigroup on a Banach space and e,f and g some functions. The initial data is taken from the Banach space D(A α ), with 0<α1 with the norm |x| α =|A α x|. Under various conditions on the functions e,f and g, the above problem admits a unique mild solution. The main techniques employed here are the Banach contraction principle and a fixed point theorem.

MSC:
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations