Weyl fractional integral
E259778
The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Weyl fractional derivative | 1 |
| Weyl fractional integral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2364680 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl fractional integral Context triple: [Riemann–Liouville integral, comparedWith, Weyl fractional integral]
-
A.
Riemann–Liouville integral
The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
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B.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
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C.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
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D.
Wigner distribution function
The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
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E.
Weyl quantization
Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weyl fractional integral Target entity description: The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
-
A.
Riemann–Liouville integral
The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
-
B.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
-
C.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
-
D.
Wigner distribution function
The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
-
E.
Weyl quantization
Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
concept in fractional calculus
ⓘ
fractional integral ⓘ mathematical operator ⓘ |
| appliesTo |
periodic boundary value problems
ⓘ
systems with long-range temporal dependence ⓘ |
| associatedWith |
convolution-type operators
ⓘ
integral transforms ⓘ |
| belongsTo |
functional analysis
ⓘ
operator theory ⓘ |
| captures |
history-dependent dynamics
ⓘ
nonlocal behavior in time ⓘ |
| definedOn |
complex-valued functions
ⓘ
real-valued functions ⓘ |
| domain |
functions on the whole real line
ⓘ
periodic functions ⓘ |
| field |
fractional calculus
ⓘ
mathematical analysis ⓘ |
| generalizes |
Riemann integral
ⓘ
classical integral ⓘ |
| hasHistoricalContext | development of fractional calculus in the 20th century ⓘ |
| hasInverseRelationWith |
Weyl fractional derivative
ⓘ
linked to:
Weyl fractional integral
|
| hasKernelType | power-law kernel ⓘ |
| hasOrder |
non-integer order
ⓘ
real order ⓘ |
| hasProperty |
compatibility with periodicity
ⓘ
translation invariance on the real line ⓘ |
| isLinear | true ⓘ |
| isNonlocal | true ⓘ |
| isSpecialCaseOf | Weyl fractional operators ⓘ |
| namedAfter | Hermann Weyl ⓘ |
| relatedTo |
Caputo fractional derivative
ⓘ
linked to:
Caputo derivative
Fourier transform methods ⓘ Riemann–Liouville fractional integral ⓘ
linked to:
Riemann–Liouville integral
|
| usedFor |
defining fractional derivatives on periodic domains
ⓘ
spectral representations of fractional operators ⓘ |
| usedIn |
control theory
ⓘ
engineering ⓘ fractional differential equations ⓘ modeling hereditary properties ⓘ modeling memory effects ⓘ physics ⓘ signal processing ⓘ viscoelasticity modeling ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Weyl fractional integral Description of subject: The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Weyl fractional integral