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)
On the maximal and minimal solutions of arbitrary-orders nonlinear functional integral and differential equations. (English) Zbl 1068.45008
The authors study the functional differential equation with retarded argument having the form $$D^\alpha_ ax(t)= f(t,x(\varphi(t))),\tag1$$ where $D^\alpha_a$ denotes the fractional derivative. Moreover, the functional integral equation of fractional order of the form $$x(t)= P(t)+ (1/\Gamma(\alpha)) \int^t_0 (t- s)^{\alpha-1} f(s,x(s))\,ds\tag2$$ is also investigated. In (2) it is assumed that $f= f(t,x)$ satisfies the classical Carathéodory conditions and $P$ is a member of the space $C[0,b]$. A few theorems on the existence of solutions of (1) and (2) are established. Some results concerning the existence of the extremal solutions and comparison type theorems concerning (2) are also derived.

45G10Nonsingular nonlinear integral equations
34K05General theory of functional-differential equations