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.
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| kernelBehavior | exponential decay of memory ⓘ |
| mathematicalNature | linear operator ⓘ |
| memoryType | exponential-type memory ⓘ |
| modifies | Caputo fractional derivative NERFINISHED ⓘ |
| namedAfter |
Mauro Fabrizio
NERFINISHED
ⓘ
Michele Caputo NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Caputo derivative NERFINISHED ⓘ Riemann–Liouville derivative NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.