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)
Geometric and physical interpretation of fractional integration and fractional differentiation. (English) Zbl 1042.26003
The author offers geometric visualizations (based on a technique called “shadows on the walls”) and physical interpretations (based on relationships between “individual time” and “cosmic time”) of important types of fractional differentiation and integration. He considers in detail the Riemann-Liouville fractional integral and derivative, the Caputo fractional derivative,the potentials of Riesz and Feller, and indicates analogues to more general convolution integrals of Volterra type and to Stieltjes integrals. While the geometric interpretations give illuminating insights into the meaning and way of acting of the operators considered, the physical interpretations presented seem to the reviewer to be of a more speculative character.

MSC:
26A33Fractional derivatives and integrals (real functions)
44A35Convolution (integral transforms)
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
83C99General relativity
45D05Volterra integral equations