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)
Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions. (English) Zbl 1213.26011

This is a survey of fractional calculus based on the fractional derivatives of the form

D a± α,β f(x)=±I a± β(1-α) d dxI a± (1-β)(1-α) f(x)·(1)

They coincide with the usual Riemann-Liouville derivatives D a± α f(x) up to finite-dimensional terms. Various known properties of such derivatives are presented together with their further developments and a number of applications.

Historical remark: Derivatives of form (1) and more general ones were first introduced and studied by M. Dzherbashyan and A. Nersesyan [Dokl. Akad. Nauk SSSR 121, 210–213 (1958; Zbl 0095.08504); Izv. Akad. Nauk Arm. SSR, Ser. Fiz.-Mat. Nauk 11, No.5, 85–106 (1958; Zbl 0086.05701)].

MSC:
26A33Fractional derivatives and integrals (real functions)
33C20Generalized hypergeometric series, p F q
33E12Mittag-Leffler functions and generalizations
47B38Operators on function spaces (general)
47G10Integral operators