Grünwald–Letnikov derivative
E898517
The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Grünwald–Letnikov derivative canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10992216 — 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: Grünwald–Letnikov derivative Context triple: [Caputo derivative, relatedTo, Grünwald–Letnikov derivative]
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A.
Caputo derivative
The Caputo derivative is a commonly used definition of a fractional derivative that modifies the Riemann–Liouville approach to allow for more physically meaningful initial conditions in differential equations.
-
B.
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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C.
Weyl fractional integral
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.
-
D.
Dini derivative
The Dini derivative is a generalized notion of derivative that captures one-sided limiting rates of change of a function, even at points where the classical derivative may not exist.
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E.
Hadamard fractional integral
The Hadamard fractional integral is a generalization of the classical integral that defines fractional-order integration using logarithmic kernels, particularly suited to functions defined on multiplicative (e.g., positive real) domains.
- 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: Grünwald–Letnikov derivative Target entity description: The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
-
A.
Caputo derivative
The Caputo derivative is a commonly used definition of a fractional derivative that modifies the Riemann–Liouville approach to allow for more physically meaningful initial conditions in differential equations.
-
B.
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.
-
C.
Weyl fractional integral
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.
-
D.
Dini derivative
The Dini derivative is a generalized notion of derivative that captures one-sided limiting rates of change of a function, even at points where the classical derivative may not exist.
-
E.
Hadamard fractional integral
The Hadamard fractional integral is a generalization of the classical integral that defines fractional-order integration using logarithmic kernels, particularly suited to functions defined on multiplicative (e.g., positive real) domains.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
fractional derivative definition
ⓘ
mathematical concept ⓘ notion in fractional calculus ⓘ |
| alternativeName | Grünwald–Letnikov fractional derivative NERFINISHED ⓘ |
| approximatedBy | fractional finite difference schemes ⓘ |
| basedOn |
finite differences
ⓘ
limit process ⓘ |
| category | nonlocal derivative ⓘ |
| characterizedBy | limit of fractional difference quotients ⓘ |
| defines | fractional order derivative ⓘ |
| domain |
complex-valued functions
ⓘ
real-valued functions ⓘ |
| equivalentTo | Riemann–Liouville derivative under suitable conditions ⓘ |
| field | fractional calculus ⓘ |
| generalizes | integer order derivative ⓘ |
| hasKernel | power-law type weighting ⓘ |
| hasRepresentation | infinite series ⓘ |
| hasType |
left-sided fractional derivative
ⓘ
right-sided fractional derivative ⓘ |
| introducedIn | 19th century ⓘ |
| mathematicalDiscipline |
analysis
ⓘ
operator theory ⓘ |
| namedAfter |
Aleksandr Letnikov
NERFINISHED
ⓘ
Alfred Grünwald NERFINISHED ⓘ |
| order |
complex order
ⓘ
real order ⓘ |
| property |
depends on function history
ⓘ
reduces to classical derivative when order is integer ⓘ |
| relatedTo |
Caputo derivative
NERFINISHED
ⓘ
Riemann–Liouville derivative NERFINISHED ⓘ fractional difference operator ⓘ fractional integral ⓘ |
| specialCaseOf | fractional difference calculus ⓘ |
| timeDomain | nonlocal operator ⓘ |
| usedFor |
modeling hereditary phenomena
ⓘ
modeling memory effects ⓘ |
| usedIn |
anomalous diffusion modeling
ⓘ
control theory ⓘ discrete-time fractional systems ⓘ fractional-order dynamical systems ⓘ numerical methods for fractional differential equations ⓘ signal processing ⓘ viscoelasticity modeling ⓘ |
| uses |
backward difference operator
ⓘ
binomial coefficients ⓘ discrete convolution sum ⓘ fractional order α ⓘ |
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: Grünwald–Letnikov derivative Description of subject: The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.