Caputo–Fabrizio derivative
E899969
The Caputo–Fabrizio derivative is a non-singular kernel formulation of fractional differentiation that modifies the classical Caputo approach to better model memory effects in physical and engineering systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Caputo–Fabrizio derivative canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10992226 — 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: Caputo–Fabrizio derivative Context triple: [Caputo derivative, hasVariant, Caputo–Fabrizio 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.
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B.
Grünwald–Letnikov derivative
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.
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C.
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.
-
D.
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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E.
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.
- 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: Caputo–Fabrizio derivative Target entity description: The Caputo–Fabrizio derivative is a non-singular kernel formulation of fractional differentiation that modifies the classical Caputo approach to better model memory effects in physical and engineering systems.
-
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.
Grünwald–Letnikov derivative
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
fractional derivative
ⓘ
mathematical operator ⓘ nonlocal operator ⓘ |
| actsOn | sufficiently smooth functions ⓘ |
| advantage |
avoids singular integrals at the lower limit
ⓘ
often easier numerical implementation than singular-kernel derivatives ⓘ |
| applicationType |
modeling of nonlocal temporal behavior
ⓘ
modeling of systems with finite memory ⓘ |
| classification | non-singular fractional derivative ⓘ |
| comparedTo |
Caputo fractional derivative
ⓘ
linked to:
Caputo derivative
|
| contrastWith | power-law kernel fractional derivatives ⓘ |
| domain |
functions defined on an interval of the real line
ⓘ
real-valued functions of time ⓘ |
| field |
applied mathematics
ⓘ
engineering ⓘ fractional calculus ⓘ mathematical physics ⓘ |
| hasKernelType |
exponential kernel
ⓘ
non-singular kernel ⓘ |
| hasParameter |
fractional order parameter alpha
ⓘ
normalization constant depending on alpha ⓘ |
| introducedBy |
Mauro Fabrizio
NERFINISHED
ⓘ
Michele Caputo ⓘ |
| kernelBehavior | exponential decay of memory ⓘ |
| mathematicalNature | linear operator ⓘ |
| memoryType | exponential-type memory ⓘ |
| modifies |
Caputo fractional derivative
ⓘ
linked to:
Caputo derivative
|
| namedAfter |
Mauro Fabrizio
NERFINISHED
ⓘ
Michele Caputo ⓘ |
| orderParameter | fractional order between 0 and 1 ⓘ |
| property |
captures fading memory
ⓘ
no power-law singularity at the origin ⓘ non-local in time ⓘ non-singular memory kernel ⓘ |
| purpose |
to avoid singular kernels in fractional differentiation
ⓘ
to model memory effects in engineering systems ⓘ to model memory effects in physical systems ⓘ |
| relatedConcept |
Atangana–Baleanu derivative
ⓘ
Caputo derivative ⓘ Riemann–Liouville derivative ⓘ |
| usedFor |
fractional differential equations
ⓘ
initial value problems with memory ⓘ |
| usedIn |
control theory with fractional dynamics
ⓘ
diffusion processes with memory ⓘ heat conduction with memory ⓘ signal processing with memory effects ⓘ viscoelasticity modeling ⓘ |
| yearProposed | 2015 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Caputo–Fabrizio derivative Description of subject: The Caputo–Fabrizio derivative is a non-singular kernel formulation of fractional differentiation that modifies the classical Caputo approach to better model memory effects in physical and engineering systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.