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)
Time-fractional telegraph equations and telegraph processes with Brownian time. (English) Zbl 1049.60062
The Fourier transforms of the fundamental solutions of the time-fractional telegraph equation 2α u t 2α +2λ α u t α =c 2 2 u x 2 , 0<α1, with initial conditions u(x,0)=δ(x) for 0<α1/2 and u(x,0)=δ(x), u t (x,0)=0 for 1/2<α1, are determined in terms of Mittag-Leffler functions. In the case α=1/2, the fundamental solution is shown to be the distribution of a telegraph process with Brownian time. In the special case c,λ such that c 2 /λ1, this distribution turns out to be a law of the iterated Brownian motion.
60H30Applications of stochastic analysis
33E12Mittag-Leffler functions and generalizations
42A61Probabilistic methods in Fourier analysis
26A33Fractional derivatives and integrals (real functions)
60G52Stable processes